DocomintQuadratic Equation Solver
Solve ax² + bx + c = 0 for x, including complex roots when the discriminant is negative.
Solves any quadratic equation using the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a, and reports which of the three root cases applies: two real roots (positive discriminant), one repeated real root (zero discriminant), or two complex roots (negative discriminant) — rather than just erroring out on the case most calculators skip.
Example: For 2x² − 4x − 6 = 0 (a=2, b=−4, c=−6), the discriminant is 64, giving two real roots: x = 3 and x = −1. For x² + 2x + 5 = 0, the discriminant is −16, giving the complex roots x = −1 + 2i and x = −1 − 2i instead.
How it works
- Enter a, b, and c from ax² + bx + c = 0
- Press Solve
- Both roots appear instantly, computed on your device via the quadratic formula
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a, for any equation in the form ax² + bx + c = 0. The ± means there are generally two solutions, one from adding the square root and one from subtracting it.
What does a negative discriminant mean?
The discriminant (b² − 4ac) being negative means the equation has no real roots — the parabola never crosses the x-axis. The two solutions still exist, but as a complex conjugate pair (a + bi and a − bi) rather than real numbers.
Is my numbers uploaded anywhere?
No — Quadratic Equation Solver runs entirely in your browser using JavaScript/WebAssembly. Your numbers is never sent to a server.