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:

(2 x - 3 + 2 x + 1) (x + 4) / 2 = 266 2 x^{2} + 7 x - 270 = 0 a = 2; b = 7; c = - 270 D = b^{2} - 4 a c = 7^{2} - 4 \cdot 2 \cdot (- 270) = 2209 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 7 \pm 2 2 0 9}{4} x_{1, 2} = \frac{- 7 \pm 4 7}{4} x_{1, 2} = - 1.75 \pm 11.75 x_{1} = 10 x_{2} = - 13.5 Factored form of the equation: 2 (x - 10) (x + 13.5) = 0

Solution in text:

2x²+7x-270=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 2209
D > 0 ... The equation has two distinct real roots

x₁ = 10
x₂ = -13.5

P = {10; -13.5}