Overview
What Is a Quadratic Equation Calculator?
This tool solves equations in the form ax² + bx + c = 0 using the quadratic formula, showing both real and complex roots.
Solve quadratic equations instantly.
Solve ax² + bx + c = 0
This tool solves equations in the form ax² + bx + c = 0 using the quadratic formula, showing both real and complex roots.
Useful for checking homework, understanding root behavior, or quickly solving quadratic equations.
Input the three coefficients from your equation.
The solutions update automatically.
x = (-b ± √(b²-4ac)) ÷ 2a
It determines the nature of the roots: positive means two real roots, zero means one repeated real root, negative means two complex roots.
The equation isn't quadratic in that case - it becomes linear (bx+c=0), which this calculator doesn't solve.
Roots involving the imaginary unit i (√-1), which occur when the discriminant is negative.
Yes, this is a common use case for verifying manual quadratic equation solutions.
It means the parabola touches the x-axis at exactly one point (the vertex sits on the x-axis).
Factoring is one method to solve quadratics; the quadratic formula works universally, including when factoring isn't straightforward.
Yes, decimal coefficients are fully supported.
No, calculations happen entirely in your browser.
Yes, completely free with no sign-up required.