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:

12 = 1 / 2 * 0.5 x * (x + 2) - 0.25 x^{2} - 0.5 x + 12 = 0 0.25 x^{2} + 0.5 x - 12 = 0 a = 0.25; b = 0.5; c = - 12 D = b^{2} - 4 a c = 0 . 5^{2} - 4 \cdot 0.25 \cdot (- 12) = 12.25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 0 . 5 \pm 1 2 . 2 5}{0 . 5} = - 1 \pm 49 x_{1, 2} = - 1 \pm 7 x_{1} = 6 x_{2} = - 8 Factored form of the equation: 0.25 (x - 6) (x + 8) = 0

Solution in text:

-0.25x²-0.5x+12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 12.25
D > 0 ... The equation has two distinct real roots

x₁ = 6
x₂ = -8

P = {6; -8}