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:

240 * (a + 4) - 2 * a * (a + 4) = 240 * a - 2 a^{2} - 8 a + 960 = 0 2 a^{2} + 8 a - 960 = 0 2 . . . prime number 8 = 2^{3} 960 = 2^{6} \cdot 3 \cdot 5 GCD (2, 8, 960) = 2 = 2 a^{2} + 4 a - 480 = 0 p = 1; q = 4; r = - 480 D = q^{2} - 4 p r = 4^{2} - 4 \cdot 1 \cdot (- 480) = 1936 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 4 \pm 1 9 3 6}{2} a_{1, 2} = \frac{- 4 \pm 4 4}{2} a_{1, 2} = - 2 \pm 22 a_{1} = 20 a_{2} = - 24 Factored form of the equation: (a - 20) (a + 24) = 0

Solution in text:

-2a²-8a+960=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 7744
D > 0 ... The equation has two distinct real roots

a₁ = 20
a₂ = -24

P = {20; -24}