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:

- 3 x^{2} - 2 * 36 * x + 36 * 36 = 0 - 3 x^{2} - 72 x + 1296 = 0 3 x^{2} + 72 x - 1296 = 0 3 . . . prime number 72 = 2^{3} \cdot 3^{2} 1296 = 2^{4} \cdot 3^{4} GCD (3, 72, 1296) = 3 = 3 x^{2} + 24 x - 432 = 0 a = 1; b = 24; c = - 432 D = b^{2} - 4 a c = 2 4^{2} - 4 \cdot 1 \cdot (- 432) = 2304 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 4 \pm 2 3 0 4}{2} x_{1, 2} = \frac{- 2 4 \pm 4 8}{2} x_{1, 2} = - 12 \pm 24 x_{1} = 12 x_{2} = - 36 Factored form of the equation: (x - 12) (x + 36) = 0

Solution in text:

-3x²-72x+1296=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 20736
D > 0 ... The equation has two distinct real roots

x₁ = 12
x₂ = -36

P = {12; -36}