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^{2} + 10 x - 11 = 0 - 2 x^{2} + 10 x - 11 = 0 2 x^{2} - 10 x + 11 = 0 a = 2; b = - 10; c = 11 D = b^{2} - 4 a c = 1 0^{2} - 4 \cdot 2 \cdot 11 = 12 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 0 \pm 1 2}{4} = \frac{1 0 \pm 2 3}{4} x_{1, 2} = 2.5 \pm 0.866025 x_{1} = 3.366025404 x_{2} = 1.633974596 Factored form of the equation: 2 (x - 3.366025404) (x - 1.633974596) = 0

Solution in text:

-2x²+10x-11=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 12
D > 0 ... The equation has two distinct real roots

x₁ = 3.3660254
x₂ = 1.6339746

P = {3.3660254; 1.6339746}