To solve for x in the equation x = 6/(2x-8), we first need to get rid of the fraction by multiplying both sides of the equation by (2x-8):

x(2x-8) = 6
2x^2 - 8x = 6

Now, rearrange the equation to set it equal to zero:

2x^2 - 8x - 6 = 0

Next, use the quadratic formula to solve for x:

x = (-(-8) ± √((-8)^2 - 4(2)(-6)))/(2(2))
x = (8 ± √(64 + 48))/4
x = (8 ± √112)/4
x = (8 ± 4√7)/4
x = 2 ± √7

Therefore, x can be either 2 + √7 or 2 - √7.