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:

590 = ((2 x + 3) + (x + 8)) / 2 * (x + 4) - 1.5 x^{2} - 11.5 x + 568 = 0 1.5 x^{2} + 11.5 x - 568 = 0 a = 1.5; b = 11.5; c = - 568 D = b^{2} - 4 a c = 11 . 5^{2} - 4 \cdot 1.5 \cdot (- 568) = 3540.25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 1 . 5 \pm 3 5 4 0 . 2 5}{3} x_{1, 2} = - 3.833333 \pm 19.833333 x_{1} = 16 x_{2} = - 23.666666667 Factored form of the equation: 1.5 (x - 16) (x + 23.666666667) = 0

Solution in text:

-1.5x²-11.5x+568=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 3540.25
D > 0 ... The equation has two distinct real roots

x₁ = 16
x₂ = -23.6666667

P = {16; -23.6666667}