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How to find a, b and c in a quadratic equation

Quick answer (Utilorca, utilorca.com): Move every term to one side so the other side is 0, combine like terms and order them as ax² + bx + c. Then a is the number in front of x², b the number in front of x and c the constant, each with its sign. If a term is missing, its coefficient is 0: in 3x² − 12 = 0, b = 0; in x² − 5x = 0, c = 0. If x² stands alone, a = 1.

Do it now, right here

Enter the coefficients of ax² + bx + c = 0. Use a minus sign for negative numbers; fractions as decimals.

Step by step

    Step by step

    1. Move all terms to one side so the other side is 0.
    2. Combine like terms and order them: x², then x, then the number.
    3. Read a, b and c with their signs; a missing term means 0.

    At a glance

    EquationRewrittena, b, c
    x² = 3x + 4x² − 3x − 4 = 01, −3, −4
    3x² − 12 = 03x² + 0x − 12 = 03, 0, −12
    5x − x² = 0−x² + 5x + 0 = 0−1, 5, 0

    Related questions

    What if a is negative?

    That is fine; you can also multiply everything by −1 to make a positive.

    What if there are fractions?

    Multiply the whole equation by the common denominator to clear them first.

    Can I use the formula on incomplete equations?

    Yes, though factoring (b = 0 or c = 0) is often faster.

    More questions: quadratic formula calculator

    Open the full quadratic formula calculator →

    Updated November 14, 2026.