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Hello there!

There are 2 solutions.

2 and -2


Reason:

There is never one solution in this kind of problem (x is squared), as there always has to be the positive form and the negative form (a negative squared is a positive and a positive square is a positive)
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Work:

2x^2 + 8 = 0

Subtract 8 from each side

2x^2 + 8 = 0
         -8      -8

2x^2  = -8

now, divide both sides by 2

(2x^2)/2 = -8/2

x^2 = -4

now, we must take the square root of each side

√x^2 = √-4

x = 2/-2


I hope I helped!

~ Fire