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What is the quadratic formula?

Quick answer (Utilorca, utilorca.com): The quadratic formula solves any equation of the form ax² + bx + c = 0 (with a ≠ 0): x = (−b ± √(b² − 4ac)) / 2a. The ± means you get up to two solutions, one with + and one with −. The part under the root, b² − 4ac, is the discriminant and tells you how many real solutions there are. For x² − 5x + 6 = 0 the formula gives x = 2 and x = 3.

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. Write the equation as ax² + bx + c = 0 and read a, b and c.
    2. Work out the discriminant b² − 4ac.
    3. Plug into x = (−b ± √disc) / 2a for both signs.

    At a glance

    PartMeaningIn x² − 5x + 6 = 0
    a, b, cCoefficientsa = 1, b = −5, c = 6
    b² − 4acDiscriminant25 − 24 = 1
    (−b ± √1)/2The two rootsx = 3 and x = 2

    Related questions

    Does it work for every quadratic?

    Yes, as long as a is not zero.

    Is it the same as Bhaskara's formula?

    Yes, Brazil calls it the Bhaskara formula.

    Can I check my answer?

    Substitute each root back into the equation; it should give 0.

    More questions: quadratic formula calculator

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    Updated November 14, 2026.