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Quadratic equation solver

Find real or complex roots from three coefficients.

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Quadratic equation solver processes your input in this browser. Inputs and results are excluded from analytics. Recent tools save tool names, visit counts and last-visit times. Saved tools store only their names. Draft saving is optional and stays on this device; delete saved text with the draft controls. Loading text from a URL is optional and contacts that server; its URL and your IP address are visible to the server. An optional “Use in” action keeps a handoff in this tab. The next tool removes it on arrival and ignores it if more than a minute has passed.

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Answer

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For ax² + bx + c = 0, the roots come from (−b ± √(b² − 4ac)) ÷ 2a. A numerically stable equivalent reduces cancellation for distinct real roots.

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Precision and calculation record
Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.
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Formula and assumptions
Enter coefficients, including zero. Negative discriminants produce complex conjugate roots; a zero leading coefficient reduces the problem to a linear equation. Nearly repeated roots can be sensitive to input precision.
Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.
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Using Quadratic equation solver
For ax² + bx + c = 0, the roots come from (−b ± √(b² − 4ac)) ÷ 2a. A numerically stable equivalent reduces cancellation for distinct real roots.
Enter coefficients, including zero. Negative discriminants produce complex conjugate roots; a zero leading coefficient reduces the problem to a linear equation. Nearly repeated roots can be sensitive to input precision.
Next: Algebra calculator
A worked example
With coefficient a of x² = 1, coefficient b of x = -5, constant c = 6, the roots is 2, 3.
Next: System of equations solver
Before you use the result
Enter coefficients, including zero. Negative discriminants produce complex conjugate roots; a zero leading coefficient reduces the problem to a linear equation. Nearly repeated roots can be sensitive to input precision.
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ToolOctopus. “Quadratic equation solver.” Updated 2026-09-26. https://tooloctopus.com/quadratic-equation-solver.
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