What are the solutions of 2x^2+3x=-8

The equation given above is written here below with all the terms transposed to only one side of the equation.

2x² + 3x + 8 = 0

The quadratic formula used for the determination of the roots is,

x = (-b + / - sqrt (b² - 4ac)) / 2a

In the quadratic equation above, we have the numerical coefficients.

a = 2

b = 3

c = 8

Substituting the known values,

x = (-3 + / - sqrt (3² - 4 (2) (8)) / (2) (2)

x = - 0.75 + 1.854i and x = - 0.75 - 1.854i

By the calculated roots above, it is known that the roots are imaginary.