All tools · 📊 Math

📊 Quadratic Equation Solver

Enter coefficients a, b, c — we solve ax² + bx + c = 0 for both real and complex roots. Shows the discriminant, vertex (h, k), and axis of symmetry.

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Examples

Two real roots
Inputx² − 3x + 2 = 0
Outputx = 1, x = 2
One repeated root
Inputx² − 4x + 4 = 0
Outputx = 2 (double root)
Complex roots
Inputx² + x + 1 = 0
Outputx = −0.5 ± 0.866i

Frequently asked questions

What does the discriminant tell me?

b² − 4ac. Positive: two real roots. Zero: one repeated root. Negative: two complex conjugate roots.

When is the quadratic formula better than factoring?

Always works. Factoring is faster when the roots are integers — but for messy coefficients, the formula is more reliable.

How is vertex form useful?

y = a(x − h)² + k tells you the parabola's peak/trough at (h, k) directly — useful for projectile motion, optimization problems.

About this tool

Quadratic Equation Solver runs entirely in your browser using standard Web APIs. No data is sent to any server. The source for this tool is in our public GitHub repository.

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Why this tool

vs typical free web-tool sites

1vwTypical free site
PriceFreeFree
Signup requiredNoOften (for premium features)
Ads inside the toolNoYes (banner + video)
Data sent to serverNo (browser-only)Yes (inputs analyzed for ads)
Total tools96Often <20 or scattered across sites
Bookmarkable URL per toolYesMixed
Loads in under 1sYes (static)Often slow (ad tracking)
MultilingualEN / ES / PT / FR / DEUsually EN only
Open sourceYesNo