ax² + bx + c = 0

Quadratic Equation Solver

Enter the coefficients a, b and c and get both roots instantly, with the discriminant and full step-by-step work shown.

2x2 − 3x − 5 = 0
–x₁
–x₂

    How it works

    1

    Enter the coefficients

    Type in a, b and c from your equation in the form ax² + bx + c = 0.

    2

    Check the discriminant

    The tool computes b² − 4ac, which decides whether the roots are real or complex.

    3

    Read the roots and steps

    Get both solutions instantly, plus every step of the quadratic formula worked out.

    FAQ

    What if the discriminant is negative?

    A negative discriminant means the equation has no real roots. The two solutions are complex conjugates, shown in the form p ± qi.

    What happens if a is 0?

    If a is 0 the equation is no longer quadratic — it becomes the linear equation bx + c = 0, which this tool solves directly for x when b is not also 0.

    How is the discriminant used?

    The discriminant, b² − 4ac, tells you the nature of the roots before you even compute them: positive gives two real roots, zero gives one repeated real root, and negative gives two complex roots.

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