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:

a (84 - 4 - a) = 64 / 4 - a^{2} + 80 a - 16 = 0 a^{2} - 80 a + 16 = 0 p = 1; q = - 80; r = 16 D = q^{2} - 4 p r = 8 0^{2} - 4 \cdot 1 \cdot 16 = 6336 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{8 0 \pm 6 3 3 6}{2} = \frac{8 0 \pm 2 4 1 1}{2} a_{1, 2} = 40 \pm 39.799497 a_{1} = 79.799497484 a_{2} = 0.200502516 Factored form of the equation: (a - 79.799497484) (a - 0.200502516) = 0

Solution in text:

-a²+80a-16=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 6336
D > 0 ... The equation has two distinct real roots

a₁ = 79.7994975
a₂ = 0.2005025

P = {79.7994975; 0.2005025}