Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

x^{2} - 1 = 5 x x^{2} - 5 x - 1 = 0 a = 1; b = - 5; c = - 1 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 1 \cdot (- 1) = 29 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 2 9}{2} x_{1, 2} = 2.5 \pm 2.692582 x_{1} = 5.192582404 x_{2} = - 0.192582404 Factored form of the equation: (x - 5.192582404) (x + 0.192582404) = 0

Solution in text:

x²-5x-1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 29
D > 0 ... The equation has two distinct real roots

x₁ = 5.1925824
x₂ = -0.1925824

P = {5.1925824; -0.1925824}