First, we will expand the expression:

(x-2)^2 = (x-2)(x-2) = x^2 - 4x + 4
4(x^2-4) = 4x^2 - 16

So, the equation becomes:

x^2 - 4x + 4 - 4x^2 + 16 + 64 = 0
-x^2 - 4x + 84 = 0

Now we can solve this quadratic equation by using the quadratic formula:

x = (-(-4) ± sqrt((-4)^2 - 4(-1)(84)))/2(-1)
x = (4 ± sqrt(16 + 336))/(-2)
x = (4 ± sqrt(352))/(-2)
x = (4 ± 18.8)/(-2)

Therefore, the solutions are:
x = (4 + 18.8)/(-2) = 11.4/(-2) = -5.7
x = (4 - 18.8)/(-2) = -14.8/(-2) = 7.4

So, the solutions to the equation are x = -5.7 and x = 7.4.