To solve this equation, we need to simplify each side of the equation first.

First, we simplify the left side:
(4x-51)/3 - (17-3x)/4

Multiplying each term by the respective denominator to get rid of the fractions:
4(4x-51)/3 - 3(17-3x)/4
(16x - 204)/3 - (51 - 3x)/4
(16x - 204)/3 - (51 - 3x)/4

Now simplify the right side:
(x+5)/2

Now the equation becomes:
(16x - 204)/3 - (51 - 3x)/4 = (x+5)/2

To get rid of the denominators, we need to multiply both sides by the least common multiple of the denominators, which is 12:
12[(16x - 204)/3] - 12[(51 - 3x)/4] = 12[(x+5)/2]

Now simplify both sides:
4(16x - 204) - 3(51 - 3x) = 6(x+5)
64x - 816 - 153 + 9x = 6x + 30
73x - 969 = 6x + 30

Now, isolate x by moving all terms with x to one side of the equation:
73x - 6x = 969 + 30
67x = 999
x = 999/67

Therefore, x = 15.