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:

- 10 * 2 - b^{2} + 9 * b = 0 - b^{2} + 9 b - 20 = 0 b^{2} - 9 b + 20 = 0 p = 1; q = - 9; r = 20 D = q^{2} - 4 p r = 9^{2} - 4 \cdot 1 \cdot 20 = 1 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{9 \pm 1}{2} b_{1, 2} = \frac{9 \pm 1}{2} b_{1, 2} = 4.5 \pm 0.5 b_{1} = 5 b_{2} = 4 Factored form of the equation: (b - 5) (b - 4) = 0

Solution in text:

-b²+9b-20=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1
D > 0 ... The equation has two distinct real roots

b₁ = 5
b₂ = 4

P = {5; 4}