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:

(x - 2 x)^{2} + (2 x - 1)^{2} = 2 5 x^{2} - 4 x - 1 = 0 a = 5; b = - 4; c = - 1 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 5 \cdot (- 1) = 36 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 3 6}{1 0} x_{1, 2} = \frac{4 \pm 6}{1 0} x_{1, 2} = 0.4 \pm 0.6 x_{1} = 1 x_{2} = - 0.2 Factored form of the equation: 5 (x - 1) (x + 0.2) = 0

Solution in text:

5x²-4x-1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 36
D > 0 ... The equation has two distinct real roots

x₁ = 1
x₂ = -0.2

P = {1; -0.2}