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 (504 + 6 x) = 720 x 6 x^{2} - 216 x = 0 6 = 2 \cdot 3 216 = 2^{3} \cdot 3^{3} 0 = 0 GCD (6, 216, 0) = 2 \cdot 3 = 6 x^{2} - 36 x = 0 a = 1; b = - 36; c = 0 D = b^{2} - 4 a c = 3 6^{2} - 4 \cdot 1 \cdot 0 = 1296 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{3 6 \pm 1 2 9 6}{2} x_{1, 2} = \frac{3 6 \pm 3 6}{2} x_{1, 2} = 18 \pm 18 x_{1} = 36 x_{2} = 0 Factored form of the equation: (x - 36) x = 0

Solution in text:

6x²-216x=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 46656
D > 0 ... The equation has two distinct real roots

x₁ = 36
x₂ = 0

P = {36; 0}