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 * v = (v + 8) * (240 - v) v^{2} + 8 v - 1920 = 0 a = 1; b = 8; c = - 1920 D = b^{2} - 4 a c = 8^{2} - 4 \cdot 1 \cdot (- 1920) = 7744 D > 0 v_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 8 \pm 7 7 4 4}{2} v_{1, 2} = \frac{- 8 \pm 8 8}{2} v_{1, 2} = - 4 \pm 44 v_{1} = 40 v_{2} = - 48 Factored form of the equation: (v - 40) (v + 48) = 0

Solution in text:

v²+8v-1920=0 ... quadratic equation

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

v₁ = 40
v₂ = -48

P = {40; -48}