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:

1^{2} + x^{2} = (1 - x)^{2} + (1 - x)^{2} - x^{2} + 4 x - 1 = 0 x^{2} - 4 x + 1 = 0 a = 1; b = - 4; c = 1 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot 1 = 12 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 1 2}{2} = \frac{4 \pm 2 3}{2} x_{1, 2} = 2 \pm 1.732051 x_{1} = 3.732050808 x_{2} = 0.267949192 Factored form of the equation: (x - 3.732050808) (x - 0.267949192) = 0

Solution in text:

-x²+4x-1=0 ... quadratic equation

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

x₁ = 3.7320508
x₂ = 0.2679492

P = {3.7320508; 0.2679492}