Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

96 = (4 + v) * v / 2 - 0.5 v^{2} - 2 v + 96 = 0 0.5 v^{2} + 2 v - 96 = 0 a = 0.5; b = 2; c = - 96 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 0.5 \cdot (- 96) = 196 D > 0 v_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 \pm 1 9 6}{1} = - 2 \pm 141 v_{1, 2} = - 2 \pm 14 v_{1} = 12 v_{2} = - 16 Factored form of the equation: 0.5 (v - 12) (v + 16) = 0

Solution in text:

-0.5v²-2v+96=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 196
D > 0 ... The equation has two distinct real roots

v₁ = 12
v₂ = -16

P = {12; -16}