First, let's simplify the expression:

2(x-6x)^2 + 120(x-3)^2 = 2(-5x)^2 + 120(x-3)^2
= 2(25x^2) + 120(x^2 - 6x - 3x + 9)
= 50x^2 + 120(x^2 - 9x + 9)

Now, distribute the 120:

50x^2 + 120x^2 - 1080x + 1080

Combine like terms:

170x^2 - 1080x + 1080 = 8

Subtract 8 from both sides:

170x^2 - 1080x + 1072 = 0

Now we have a quadratic equation:

170x^2 - 1080x + 1072 = 0

We can simplify this equation further by dividing by 2:

85x^2 - 540x + 536 = 0

Now you can either use the quadratic formula, factoring, or another method to solve for x.