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:

20 * (x - 8) + 20 * x = (x - 8) * x - x^{2} + 48 x - 160 = 0 x^{2} - 48 x + 160 = 0 a = 1; b = - 48; c = 160 D = b^{2} - 4 a c = 4 8^{2} - 4 \cdot 1 \cdot 160 = 1664 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 8 \pm 1 6 6 4}{2} = \frac{4 8 \pm 8 2 6}{2} x_{1, 2} = 24 \pm 20.396078 x_{1} = 44.396078054 x_{2} = 3.603921946 Factored form of the equation: (x - 44.396078054) (x - 3.603921946) = 0

Solution in text:

-x²+48x-160=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1664
D > 0 ... The equation has two distinct real roots

x₁ = 44.3960781
x₂ = 3.6039219

P = {44.3960781; 3.6039219}