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} + 3 x - 9 = 0 x^{2} + 3 x - 9 = 0 a = 1; b = 3; c = - 9 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 1 \cdot (- 9) = 45 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 \pm 4 5}{2} = \frac{- 3 \pm 3 5}{2} x_{1, 2} = - 1.5 \pm 3.354102 x_{1} = 1.854101966 x_{2} = - 4.854101966 Factored form of the equation: (x - 1.854101966) (x + 4.854101966) = 0

Solution in text:

x²+3x-9=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 45
D > 0 ... The equation has two distinct real roots

x₁ = 1.854102
x₂ = -4.854102

P = {1.854102; -4.854102}