AI Quadratic Formula Solver

x = (-b ± √(b² - 4ac))/(2a). Step-by-step, every time.

AskSia applies the quadratic formula to any ax² + bx + c = 0 step-by-step. Coefficients identified, discriminant computed and interpreted, radical simplified, and both roots returned in exact and decimal form. A parabola sketch with the roots and vertex labeled appears on every solve.

Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
Quick Answer

What is the AskSia quadratic formula solver?

The AskSia quadratic formula solver applies x = (-b ± √(b² - 4ac))/(2a) to any quadratic equation step-by-step. AskSia identifies a, b, and c, computes the discriminant b² - 4ac, and interprets its sign: positive means two real roots, zero means one repeated root, negative means two complex conjugate roots. The radical is simplified, the plus and minus cases are computed separately, and the roots are given in both exact (simplified radical) and decimal form. A parabola sketch with both roots, the vertex, and the axis of symmetry labeled appears alongside.

98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver

The formula, fully unpacked, every time.

Most quadratic formula mistakes come from sign errors on negative b or arithmetic slips in the discriminant. AskSia handles both cleanly, with the work shown.

Coefficients identified first

AskSia writes ax² + bx + c = 0 and labels a, b, and c explicitly before substituting. This catches the common mistake of forgetting that b is negative when the equation reads x² - 5x + 6 = 0 (where b = -5, not 5).

a, b, c labeled

Discriminant computed and interpreted

b² - 4ac is computed step-by-step, with signs tracked carefully. The result is then interpreted: positive gives two real roots, zero gives one repeated root, negative gives two complex conjugate roots. The interpretation appears before the radical step.

Discriminant first

Radical simplified

When the discriminant is not a perfect square, AskSia simplifies the radical by factoring out perfect squares. For example, √48 becomes 4√3. The simplified form appears in the final exact answer.

Radical simplified

Plus and minus split

The ± in the formula is split into two separate root computations, shown side-by-side. The plus case gives one root, the minus case gives the other, with the arithmetic shown for each separately to avoid sign errors.

Both roots shown

Complex roots in a + bi

When b² - 4ac < 0, AskSia handles √(negative) by factoring out i = √(-1). The two complex conjugate roots are returned as p + qi and p - qi, with p = -b/(2a) and q = √(4ac - b²)/(2a).

Complex supported

Parabola sketch with roots

Every solve includes the parabola y = ax² + bx + c with both roots labeled at the x-axis (or noted as not crossing for complex roots), the vertex at x = -b/(2a), and the axis of symmetry drawn.

Parabola included
How It Works

Three taps to the quadratic formula applied.

Step 01

Capture the equation

Snap a photo, paste the equation, or type ax² + bx + c = 0 into the built-in calculator. AskSia rearranges if needed to get it into standard form.

Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02

Watch the formula step-by-step

AskSia identifies a, b, and c, computes b² - 4ac, interprets the discriminant, simplifies the radical, and computes both the plus and minus roots. Every line is named.

Calculus · Step 4 of 4
1.4s
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03

See the parabola and answer

Both roots are returned in exact and decimal form, with the parabola sketched and the roots, vertex, and axis of symmetry labeled. Ask follow-up questions or generate practice problems.

Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On

Solve anywhere
you study.

Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.

Web App

Full study studio

Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.

Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
app.asksia.ai/solver
Hi! What are we studying today?
Ask about your homework, lecture, or readings...
Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App

Snap & solve, anywhere

Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.

One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
AskSia
+
What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases

Every quadratic formula use case.

📐

Algebra 1 and 2 homework

Daily quadratic problems where factoring isn't clean. AskSia applies the formula with every step named, useful when your teacher wants the formula shown explicitly.

Algebra 1 and 2
⚛️

Complex roots in College Algebra

When the discriminant is negative, AskSia handles complex (imaginary) roots cleanly in a + bi form, with both conjugates shown and the imaginary unit tracked carefully.

Complex roots
🧪

Word problems

Projectile motion, profit-maximization, geometry: the algebra usually reduces to ax² + bx + c = 0, and AskSia applies the formula to get the roots, then interprets them in context.

Word problems
🧬

Discriminant questions

When the problem asks 'how many real solutions does this equation have?' AskSia computes the discriminant and interprets the sign, without needing to find the roots themselves.

Discriminant only
💻

SAT, ACT, AP prep

The quadratic formula appears on SAT, ACT, AP, and IB. After any solve, generate practice problems at the right difficulty level for your target exam.

Exam prep
🎯

Check factoring vs formula

When a problem can be solved by either factoring or the formula, AskSia can show both methods side-by-side, useful for understanding why the formula always works while factoring is faster when roots are rational.

Method comparison
Compare

AskSia vs. ChatGPT,
Photomath & Symbolab.

General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.

Feature comparison between AskSia Solver and alternatives
FeatureAskSia SolverChatGPTPhoto Solvers
Solution accuracy✓ 98%~70-85%, hallucinations~90%, math only
Auto-generated diagrams✓ Every solveInconsistent / brokenGraphs only, math-only
Step-by-step explanations✓ Numbered + plain EnglishInconsistent depth✓ Math steps
Subject coverage✓ Math, Physics, Chem, Bio, CS, Econ✓ Wide but unverifiedMath only
Photo input✓ Handwriting + diagrams + codePhotos OK, weak on handwriting✓ Math photos only
Answer verification✓ Self-checked before displayNo verificationMath engine only
Tutor follow-ups✓ Hints, alt methods, ELI5✓ General chatNot available
Practice and flashcards✓ One-tap from any solveManual promptingNot available
Code debugging✓ Python, Java, C++, SQL...✓ YesNot available
Free to start✓ Daily solves, no cardLimited model accessSteps locked behind paywall
FAQ

Frequently asked questions.

How does AskSia apply the quadratic formula step-by-step?
AskSia rewrites the equation in standard form ax² + bx + c = 0, identifies and labels each coefficient (a, b, c) explicitly, computes the discriminant b² - 4ac with signs tracked carefully, interprets the discriminant's sign (positive, zero, or negative), simplifies the radical by factoring out perfect squares, splits the plus-minus into two separate root computations, and returns each root in both exact form (with simplified radical) and decimal form. Every line has a named reason, so the work is easy to copy for homework.
What does the discriminant tell me before I solve?
The discriminant b² - 4ac determines the nature of the roots before you do any arithmetic. If b² - 4ac > 0, the equation has two distinct real roots (the parabola crosses the x-axis twice). If b² - 4ac = 0, the equation has one repeated real root (the parabola touches the x-axis at the vertex). If b² - 4ac < 0, the equation has two complex conjugate roots (the parabola does not cross the x-axis). AskSia computes and interprets the discriminant before the radical step, so you know what to expect.
Does AskSia handle the quadratic formula when the discriminant is negative?
Yes. When b² - 4ac < 0, AskSia factors out i = √(-1) and returns the two complex conjugate roots in the form a + bi and a minus bi. For example, for x² + 2x + 5 = 0, the discriminant is -16, so √(-16) becomes 4i, and the roots are -1 + 2i and -1 minus 2i. The parabola sketch confirms visually that the curve does not cross the x-axis.
How does AskSia simplify the radical from the discriminant?
When the discriminant is not a perfect square, AskSia simplifies √(b² - 4ac) by factoring out the largest perfect square. For example, if b² - 4ac = 48, AskSia recognizes 48 = 16 × 3 and rewrites √48 as 4√3. The final answer is given in exact form with the simplified radical, plus the decimal approximation rounded to a reasonable number of digits, so you have both depending on what your assignment asks for.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
Start Today

Quadratic formula. Discriminant. Roots. Done.

Join 2M+ students using AskSia to apply the quadratic formula step-by-step, with the discriminant interpreted, the radical simplified, and the parabola graphed on every solve.

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