To solve this equation, follow these steps:

Distribute the multiplication on the right side of the equation:

X - (5 - x)/2 = (21 + 12x)/4
X - (5/2 - x/2) = (21 + 12x)/4
X - 5/2 + x/2 = (21 + 12x)/4

Combine like terms on the left side of the equation:

X + x/2 - 5/2 = (21 + 12x)/4
(2X + x - 5)/2 = (21 + 12x)/4

Cross multiply to get rid of the fractions:

4(2X + x - 5) = 2(21 + 12x)
8X + 4x - 20 = 42 + 24x

Combine like terms:

8X + 4x - 20 = 42 + 24x
12X - 24x = 62

Move all the terms with X to one side:

12X - 24x = 62
12X - 24x - 62 = 0

Combine like terms:

-12x - 62 = 0

Solve for x:

-12x = 62
x = -62/12
x = -31/6

Therefore, the solution to the equation is x = -31/6.