Quadratic Equation Solver
Enter a, b, and c to solve ax² + bx + c = 0 — roots, discriminant, and vertex.
Solve any quadratic instantly
A quadratic equation ax² + bx + c = 0 is the workhorse of algebra, physics, and geometry, but working the formula by hand invites sign errors. Enter the three coefficients and this returns the roots, the discriminant, and the parabola’s vertex, all computed live.
For example, x² − 3x + 2 = 0 has a discriminant of 1, giving two clean real roots at x = 1 and x = 2. When the discriminant goes negative, the tool switches to complex conjugate roots rather than failing.
Reliable and private
Every value is computed in your browser with the exact quadratic formula, and if you set a = 0 it correctly falls back to solving the linear case. Nothing you enter is uploaded.
Frequently Asked Questions
How are the roots calculated?
With the quadratic formula, x = (−b ± √(b²−4ac)) / 2a. The tool also reports the discriminant b²−4ac, which decides whether the roots are real or complex.
What does the discriminant tell me?
If it is positive there are two real roots, if zero there is one repeated real root, and if negative the two roots are complex conjugates.
Does it handle a = 0?
Yes. With a = 0 the equation is linear, so it solves bx + c = 0 instead and says so.
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