Quadratic equation calculator

Quadratic equation has the basic form:

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

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

x (6 - x) = 2^{2} - x^{2} + 6 x - 4 = 0 x^{2} - 6 x + 4 = 0 a = 1; b = - 6; c = 4 D = b^{2} - 4 a c = 6^{2} - 4 \cdot 1 \cdot 4 = 20 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{6 \pm 2 0}{2} = \frac{6 \pm 2 5}{2} x_{1, 2} = 3 \pm 2.236068 x_{1} = 5.236067977 x_{2} = 0.763932023 Factored form of the equation: (x - 5.236067977) (x - 0.763932023) = 0

Solution in text:

-x²+6x-4=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 20
D > 0 ... The equation has two distinct real roots

x₁ = 5.236068
x₂ = 0.763932

P = {5.236068; 0.763932}