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Quadratic Solver

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Quadratic Solver finds the roots of ax² + bx + c = 0 using the quadratic formula. Enter the three coefficients and the calculator shows the discriminant (b² - 4ac), nature of the roots (two real, one repeated, or two complex conjugates), and the exact root values. Useful for algebra, engineering, and physics problems. Runs entirely in your browser.

Related: Percentage CalculatorGCDPythagorean Theorem

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ax² + bx + c = 01x² − 5x + 6 = 0

Cannot be 0

two real roots (discriminant = 1)

Root 1x₁ = 3
Root 2x₂ = 2

Vertex

x-coordinate2.5
y-coordinate-0.25

Quadratic equation solver

Solves equations of the form ax² + bx + c = 0 using the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac determines the nature of the roots: positive → two real roots, zero → one repeated root, negative → two complex conjugate roots.