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Quadratic Formula Calculator

Solve any quadratic equation ax² + bx + c = 0 using the quadratic formula. Shows real and complex roots, discriminant, vertex, and graph.

Enter Coefficients

Equation: ax² + bx + c = 0

a (x² coefficient)
b (x coefficient)
c (constant)

Quick entry — enter equation like: x^2-5x+6=0

Solution
Roots
x = 3, x = 2
Two real roots
PropertyValue
Graph

Quadratic Formula

For ax² + bx + c = 0, the solutions are: x = (−b ± √(b²−4ac)) / 2a

Discriminant (Δ = b²−4ac)

Δ valueNumber of rootsType
Δ > 02 real rootsDistinct real solutions
Δ = 01 real root (repeated)Parabola touches x-axis
Δ < 00 real rootsComplex conjugate roots