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
Input
x² − 3x + 2 = 0Output
x = 1, x = 2One repeated root
Input
x² − 4x + 4 = 0Output
x = 2 (double root)Complex roots
Input
x² + x + 1 = 0Output
x = −0.5 ± 0.866iFrequently 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.
Related tools
- 📐 Triangle Calculator — Solve any triangle given 3 known parts (SSS, SAS, ASA, etc.).
- ➗ GCD / LCM Calculator — Find greatest common divisor and least common multiple of any numbers.
- 📊 Statistics Calculator — Mean, median, mode, standard deviation, variance, range from a number list.
Why this tool
vs typical free web-tool sites
| 1vw | Typical free site | |
|---|---|---|
| Price | Free | Free |
| Signup required | No | Often (for premium features) |
| Ads inside the tool | No | Yes (banner + video) |
| Data sent to server | No (browser-only) | Yes (inputs analyzed for ads) |
| Total tools | 96 | Often <20 or scattered across sites |
| Bookmarkable URL per tool | Yes | Mixed |
| Loads in under 1s | Yes (static) | Often slow (ad tracking) |
| Multilingual | EN / ES / PT / FR / DE | Usually EN only |
| Open source | Yes | No |