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:

3 x 2 - 16 x + 2 = 0 3 x^{2} - 16 x + 2 = 0 a = 3; b = - 16; c = 2 D = b^{2} - 4 a c = 1 6^{2} - 4 \cdot 3 \cdot 2 = 232 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 6 \pm 2 3 2}{6} = \frac{1 6 \pm 2 5 8}{6} x_{1, 2} = 2.666667 \pm 2.538591 x_{1} = 5.205257702 x_{2} = 0.128075631 Factored form of the equation: 3 (x - 5.205257702) (x - 0.128075631) = 0

Solution in text:

3x²-16x+2=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 232
D > 0 ... The equation has two distinct real roots

x₁ = 5.2052577
x₂ = 0.1280756

P = {5.2052577; 0.1280756}