Expanding the left side of the equation, we get:

(2x-8)^2 = (2x-8)(2x-8) = 4x^2 - 32x + 64

Expanding the right side of the equation, we get:

(x-3)(x+3) = x^2 + 3x - 3x - 9 = x^2 - 9

Putting it back into the original equation, we have:

4x^2 - 32x + 64 + x^2 - 9 = 4

Combining like terms:

5x^2 - 32x + 55 = 4

Rearranging the equation and setting it equal to zero:

5x^2 - 32x + 51 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-(-32) ± √((-32)^2 - 4(5)(51)) / 2(5)

x = (32 ± √(1024 - 1020)) / 10

x = (32 ± √4) / 10

x = (32 ± 2) / 10

x = 34/10 or 30/10

Therefore, x = 3.4 or 3.