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:

4^{2} = x * (19 - x) x^{2} - 19 x + 16 = 0 a = 1; b = - 19; c = 16 D = b^{2} - 4 a c = 1 9^{2} - 4 \cdot 1 \cdot 16 = 297 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 9 \pm 2 9 7}{2} = \frac{1 9 \pm 3 3 3}{2} x_{1, 2} = 9.5 \pm 8.616844 x_{1} = 18.11684397 x_{2} = 0.88315603 Factored form of the equation: (x - 18.11684397) (x - 0.88315603) = 0

Solution in text:

x²-19x+16=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 297
D > 0 ... The equation has two distinct real roots

x₁ = 18.116844
x₂ = 0.883156

P = {18.116844; 0.883156}