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:

360 * x = (360 + 3 * x) * (x - 4) - 3 x^{2} + 12 x + 1440 = 0 3 x^{2} - 12 x - 1440 = 0 3 . . . prime number 12 = 2^{2} \cdot 3 1440 = 2^{5} \cdot 3^{2} \cdot 5 GCD (3, 12, 1440) = 3 = 3 x^{2} - 4 x - 480 = 0 a = 1; b = - 4; c = - 480 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot (- 480) = 1936 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 1 9 3 6}{2} x_{1, 2} = \frac{4 \pm 4 4}{2} x_{1, 2} = 2 \pm 22 x_{1} = 24 x_{2} = - 20 Factored form of the equation: (x - 24) (x + 20) = 0

Solution in text:

-3x²+12x+1440=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 17424
D > 0 ... The equation has two distinct real roots

x₁ = 24
x₂ = -20

P = {24; -20}