Quadratic Equation Solver
Solve any quadratic equation ax² + bx + c = 0 using the quadratic formula, with real or complex roots, discriminant and vertex.
Result
Roots
No equation
With a and b both zero there's no variable to solve for.
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Enter the coefficients a, b and c from ax² + bx + c = 0. We'll find the roots using the quadratic formula, along with the discriminant (which tells you the type of roots) and the vertex of the parabola.
Frequently asked questions
What is the discriminant?
The discriminant is b² − 4ac, the part under the square root in the quadratic formula. If it's positive there are two real roots, if zero there's one repeated root, and if negative the roots are complex.
What if a is zero?
Then it isn't a quadratic — the x² term disappears and you're left with a linear equation bx + c = 0, which this calculator solves as a single root.