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:

45 * (12 + v) = (8 * (12 + v) - 45) * (12 - v) 8 v^{2} - 72 = 0 8 = 2^{3} 0 = 0 72 = 2^{3} \cdot 3^{2} GCD (8, 0, 72) = 2^{3} = 8 v^{2} - 9 = 0 v_{1, 2} = \pm 9 = \pm 3 v_{1} = 3 v_{2} = - 3

Solution in text:

8v²-72=0 ... b=0; pure quadratic equation

Discriminant:
D = b² - 4ac = 2304
D > 0 ... The equation has two distinct real roots

v₁ = 3
v₂ = -3

P = {3; -3}