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:

(17 + 5 * b) * b = - 6 5 b^{2} + 17 b + 6 = 0 p = 5; q = 17; r = 6 D = q^{2} - 4 p r = 1 7^{2} - 4 \cdot 5 \cdot 6 = 169 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 1 7 \pm 1 6 9}{1 0} b_{1, 2} = \frac{- 1 7 \pm 1 3}{1 0} b_{1, 2} = - 1.7 \pm 1.3 b_{1} = - 0.4 b_{2} = - 3 Factored form of the equation: 5 (b + 0.4) (b + 3) = 0

Solution in text:

5b²+17b+6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 169
D > 0 ... The equation has two distinct real roots

b₁ = -0.4
b₂ = -3

P = {-0.4; -3}