Let's first simplify the left side of the equation:

(1/4x + 5) - (-3/4 - 7)
= 1/4x + 5 + 3/4 + 7 (double negative becomes positive)
= 1/4x + 5 + 3/4 + 28/4 (convert 7 to have common denominator)
= 1/4x + 36/4 + 3/4
= 1/4x + 39/4

Now the equation becomes:

1/4x + 39/4 = 5.2

To solve for x, we can first subtract 39/4 from both sides:

1/4x = 5.2 - 39/4
1/4x = 26/5

Now we can multiply both sides by 4 to isolate x:

x = 4 * 26/5
x = 104/5

Therefore, x = 20.8.