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:

h (h - 2) = 84 h^{2} - 2 h - 84 = 0 a = 1; b = - 2; c = - 84 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 1 \cdot (- 84) = 340 D > 0 h_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 \pm 3 4 0}{2} = \frac{2 \pm 2 8 5}{2} h_{1, 2} = 1 \pm 9.219544 h_{1} = 10.219544457 h_{2} = - 8.219544457 Factored form of the equation: (h - 10.219544457) (h + 8.219544457) = 0

Solution in text:

h²-2h-84=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 340
D > 0 ... The equation has two distinct real roots

h₁ = 10.2195445
h₂ = -8.2195445

P = {10.2195445; -8.2195445}