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:

2 x^{2} - 4 x - 6 = 0 2 x^{2} - 4 x - 6 = 0 2 . . . prime number 4 = 2^{2} 6 = 2 \cdot 3 GCD (2, 4, 6) = 2 = 2 x^{2} - 2 x - 3 = 0 a = 1; b = - 2; c = - 3 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 1 \cdot (- 3) = 16 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 \pm 1 6}{2} x_{1, 2} = \frac{2 \pm 4}{2} x_{1, 2} = 1 \pm 2 x_{1} = 3 x_{2} = - 1 Factored form of the equation: (x - 3) (x + 1) = 0

Solution in text:

2x²-4x-6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 64
D > 0 ... The equation has two distinct real roots

x₁ = 3
x₂ = -1

P = {3; -1}