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    Quadratic Equation Solver

    Solve ax² + bx + c = 0 with step-by-step working: discriminant, real or complex roots, vertex and axis of symmetry. Free online quadratic formula calculator.

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    How to use Quadratic Equation Solver

    1. 1Enter the coefficients a, b and c of ax² + bx + c = 0 (use 0 for a missing term and negatives like -3)
    2. 2Read the roots instantly — real, repeated or complex — with the discriminant
    3. 3Follow the step-by-step quadratic formula working and see the vertex of the parabola

    Frequently asked questions

    What is the quadratic formula?▾

    x = (−b ± √(b² − 4ac)) / 2a. It solves any equation ax² + bx + c = 0 with a ≠ 0.

    What does the discriminant tell you?▾

    Δ = b² − 4ac. If Δ > 0 there are two different real roots, if Δ = 0 one repeated root, and if Δ < 0 two complex roots of the form p ± qi.

    What are the roots of x² − 3x + 2 = 0?▾

    Δ = 9 − 8 = 1, so x = (3 ± 1) / 2, giving x = 1 and x = 2. That matches the factorization (x − 1)(x − 2).

    How do I find the vertex?▾

    The vertex is at x = −b / 2a, and its y-value is c − b² / 4a. For x² − 3x + 2 that's (1.5, −0.25).

    Embed Quadratic Equation Solver on your website▾

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