Quadratic Equation Solver 🔒 Your data never leaves your browser.
Solve ax² + bx + c = 0, including real and complex roots.
About this tool
Any quadratic equation of the form ax² + bx + c = 0 (with a ≠ 0) can be solved with the quadratic formula: x = (−b ± √(b² − 4ac)) / (2a). The expression under the square root, the discriminant b² − 4ac, tells you what kind of roots to expect before you even take the root.
This solver handles all three cases automatically as you type: a positive discriminant gives two distinct real roots, a discriminant of exactly zero gives a single repeated real root (the parabola just touches the x-axis), and a negative discriminant gives a pair of complex conjugate roots in a ± bi form. Everything is computed instantly in your browser — nothing is ever sent anywhere.
Frequently asked questions
What does it mean when the discriminant is negative?
It means the parabola y = ax² + bx + c never crosses the x-axis — there's no real number x that makes the equation equal zero. The two solutions still exist mathematically, but as a complex-conjugate pair (a + bi and a − bi). This is normal and not an error; it simply means the equation has no real-number roots.