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Quadratic formula examples and practice problems

Quick answer (Utilorca, utilorca.com): Example 1: x² + x − 6 = 0 gives Δ = 1 + 24 = 25, so x = (−1 ± 5)/2, that is 2 or −3. Example 2: 4x² − 12x + 9 = 0 gives Δ = 144 − 144 = 0, one root x = 12/8 = 3/2. Example 3: x² − 2x + 2 = 0 gives Δ = 4 − 8 = −4, roots 1 ± i. Try the practice problems in the table, then check them by typing a, b and c above.

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. Solve each practice equation on paper.
    2. Type a, b and c into the calculator above.
    3. Compare the discriminant and roots with yours.

    At a glance

    Practice equationDiscriminantAnswer
    x² − 7x + 10 = 09x = 2 or 5
    9x² + 6x + 1 = 00x = −1/3
    x² + 6x + 13 = 0−16x = −3 ± 2i

    Related questions

    How can I check without the calculator?

    Substitute each root back in; the left side should equal 0.

    Which method should I try first?

    Look for easy factoring; if none, use the formula.

    Where can I get more problems?

    Change a, b and c above to create your own and see the steps.

    More questions: quadratic formula calculator

    Open the full quadratic formula calculator →

    Updated November 14, 2026.