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Quadratic equation solver

Solve ax² + bx + c = 0 and inspect the discriminant.

Free. No account needed.

Optional equipment

An optional suggestion for your wider workspace: a security key can be used with online accounts that support it. This tool does not require one.

You do not need to buy anything to use this free tool.

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Inputs are processed on your device. Check results before using them.

Formula, method and rounding

ax² + bx + c = 0; Δ = b² − 4ac

Scaled coefficients and a cancellation-resistant root formula improve stability. A zero quadratic coefficient becomes a linear equation.

Currency follows the rule above; other numeric results display up to 12 significant digits. Inputs are limited by JavaScript number precision. Verify results before critical use.

Result

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How it works

  1. Rewrite the equation as ax² + bx + c = 0 and enter its signed coefficients; a must be nonzero.
  2. Calculate and inspect the discriminant before reading the roots.
  3. Substitute a returned root into the original equation. A negative discriminant means there are no real roots, not that complex roots were calculated.

Example & practical use

x² − 5x + 6 = 0 has roots 2 and 3.

Limits and help

Real roots only; negative discriminants are reported explicitly.

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Troubleshooting

Check the unit for each field. Use a decimal point without thousands separators in numeric fields. A blank value is not the same as zero. Verify important results independently.

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