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:

35 = v * 0.8 + 0.5 * 6.5 * (v / 6.5)^{2} - 0.07692307692308 v^{2} - 0.8 v + 35 = 0 0.07692307692308 v^{2} + 0.8 v - 35 = 0 a = 0.076923; b = 0.8; c = - 35 D = b^{2} - 4 a c = 0 . 8^{2} - 4 \cdot 0.076923 \cdot (- 35) = 11.4092307692 D > 0 v_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 0 . 8 \pm 1 1 . 4 1}{0 . 1 5 3 8 4 6} v_{1, 2} = - 5.2 \pm 21.955409 v_{1} = 16.755409356 v_{2} = - 27.155409356 Factored form of the equation: 0.07692307692308 (v - 16.755409356) (v + 27.155409356) = 0

Solution in text:

-0.07692307692308v²-0.8v+35=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 11.4092307692
D > 0 ... The equation has two distinct real roots

v₁ = 16.7554094
v₂ = -27.1554094

P = {16.7554094; -27.1554094}