SOLUTION: Given 2x² = -8, x is .

Given  2x² = -8  IMPLIES

        x^2 = -4     (which is -8/2),


and it means that x can not be real number.


This equation HAS NO solutions in real numbers.


It has solutions in complex number domain.



In complex number domain, equation 

    x^2 = -4


has two roots

    x =  = +/- 2i,


where  " i "  is complex imaginary units   i = .


So, again, the original equation has no real roots;

it has two complex roots   2i  and  -2i.