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How to solve a quadratic equation with the formula, step by step

Quick answer (Utilorca, utilorca.com): Take 2x² + 3x − 2 = 0. First read a = 2, b = 3, c = −2. Then the discriminant: b² − 4ac = 9 − 4 × 2 × (−2) = 9 + 16 = 25. Its root is 5. Now x = (−3 ± 5) / (2 × 2): with + you get 2/4 = 1/2, with − you get −8/4 = −2. So x = 1/2 or x = −2. The calculator above shows these same steps for any a, b and c.

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. Rewrite as ax² + bx + c = 0 and note a, b, c with their signs.
    2. Compute b² − 4ac carefully (watch negative c).
    3. Apply x = (−b ± √disc) / 2a and simplify both roots.

    At a glance

    Step2x² + 3x − 2 = 0Result
    Coefficientsa = 2, b = 3, c = −2—
    Discriminant9 − 4·2·(−2)25
    Roots(−3 ± 5)/41/2 and −2

    Related questions

    What is the most common mistake?

    Losing a minus sign, especially in −4ac when c is negative, or forgetting that −b changes sign.

    Why divide by 2a and not just 2?

    The formula divides the whole numerator by 2a; with a = 2 that is 4.

    Can I factor instead?

    If the equation factors easily, yes: 2x² + 3x − 2 = (2x − 1)(x + 2).

    More questions: quadratic formula calculator

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    Updated November 14, 2026.