Quadratic formula mistakes usually start with the signs
Before using a formula, move every term to one side and identify a, b and c exactly as they appear.
Quadratic equation →Put the equation in standard form
The calculator solves ax²+bx+c = 0 with a nonzero a. For x² = 5x−6, move the right-hand terms to obtain x²−5x+6 = 0. Enter a = 1, b = −5 and c = 6. Entering b = 5 would solve a different equation. Missing terms have coefficient zero; a coefficient of 1 is still a coefficient even when the original expression omits it.
Compute and verify the roots
The discriminant is (−5)²−4×1×6 = 1. The formula gives x = (5±1)/2, so the roots are 3 and 2. Substitute into the original equation: 3² = 5×3−6 and 2² = 5×2−6. Both checks pass. Checking the original equation, rather than only the rearranged one, can catch an earlier transcription error.
Handle special cases honestly
If a = 0, the equation is linear or degenerate rather than quadratic, so this tool rejects it. Do not replace zero with a tiny arbitrary value just to get a result. Also ensure that the input is an equation, not an inequality: roots alone do not solve x²−5x+6 > 0. Inequalities require checking intervals and whether the endpoints are included. For a missing linear term, enter b=0 explicitly instead of shifting the constant into the wrong coefficient field.
Try the calculators
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