Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

x^{2} = 9 x + 1 x^{2} - 9 x - 1 = 0 a = 1; b = - 9; c = - 1 D = b^{2} - 4 a c = 9^{2} - 4 \cdot 1 \cdot (- 1) = 85 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{9 \pm 8 5}{2} x_{1, 2} = 4.5 \pm 4.609772 x_{1} = 9.109772229 x_{2} = - 0.109772229 Factored form of the equation: (x - 9.109772229) (x + 0.109772229) = 0

Solution in text:

x²-9x-1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 85
D > 0 ... The equation has two distinct real roots

x₁ = 9.1097722
x₂ = -0.1097722

P = {9.1097722; -0.1097722}