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. 

The answer is the second choice