Solve linear equations ax + b = c and quadratic equations ax² + bx + c = 0, with the discriminant and vertex shown for quadratics.
Equation Solver Calculator
Solution
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Discriminant (quadratic)
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Vertex x (quadratic)
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How it works: Linear: x = (c − b) ÷ a. Quadratic: the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant D = b² − 4ac tells you the story before you solve: D > 0 two real roots, D = 0 one repeated root, D < 0 a pair of complex roots (shown here too). The vertex of the parabola sits at x = −b ÷ 2a.
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Estimates only — results depend on the values you enter and the standard formulas shown above.