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:

16 * (v + 0.5) = 4 * (v + 0.5) + 12 * v + 20 / 60 * v * (v + 0.5) - 0.33333333333333 v^{2} - 0.167 v + 6 = 0 0.33333333333333 v^{2} + 0.167 v - 6 = 0 a = 0.333333; b = 0.167; c = - 6 D = b^{2} - 4 a c = 0.16 7^{2} - 4 \cdot 0.333333 \cdot (- 6) = 8.0277777778 D > 0 v_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 0 . 1 7 \pm 8 . 0 3}{0 . 6 6 6 6 6 7} v_{1, 2} = - 0.25 \pm 4.25 v_{1} = 4 v_{2} = - 4.5 Factored form of the equation: 0.33333333333333 (v - 4) (v + 4.5) = 0

Solution in text:

-0.33333333333333v²-0.16666666666667v+6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 8.0277777778
D > 0 ... The equation has two distinct real roots

v₁ = 4
v₂ = -4.5

P = {4; -4.5}