To simplify the expression, we need to perform the operations in the following order: parentheses, multiplication/division, and addition/subtraction.

First, let's simplify the expression inside the parentheses:
(15/4 : 1/4 + 12/5 x 5/4) - (7/2 x 4/5 - 6/5 : 3/2) / (3/2 + 3/4)

Step 1: Perform the division inside the parentheses:
(15/4 : 1/4 + 12/5 x 5/4) - (7/2 x 4/5 - 6/5 : 3/2) / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5 x 5/4) - (7/2 x 4/5 - 6/5 x 2/3) / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5 x 5/4) - (28/10 - 12/15) / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5 x 5/4) - (14/5 - 4/5) / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5 x 5/4) - (10/5) / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5 x 5/4) - 2 / (3/2 + 3/4)

Step 2: Perform the multiplication inside the parentheses:
(15/4 : 1/4 + 12/5 x 5/4) - 2 / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5 x 1) - 2 / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5) - 2 / (3/2 + 3/4)
= (15/4 : 1/4 + 12/5) - 2 / (6/4 + 3/4)
= (15/4 : 1/4 + 12/5) - 2 / (9/4)
= (15/4 : 1/4 + 12/5) - 8/9

Step 3: Perform the division inside the parentheses:
(15/4 : 1/4 + 12/5) - 8/9
= (15/4 x 4/1 + 12/5) - 8/9
= (15 + 12/5) - 8/9
= (75/5 + 12/5) - 8/9
= (87/5) - 8/9

Step 4: Perform the addition:
(87/5) - 8/9
= (87/5 x 9/9) - 8/9
= (783/45) - 8/9

Now, let's solve for x:
(783/45) - 8/9 = 64

To solve for x, we need to isolate it on one side of the equation. Let's multiply both sides by 45 to eliminate the denominators:
(783/45) - 8/9 = 64
(783/45) - 8/9 = 64(45)
783 - 40 = 2880
743 = 2880

Since the equation is not true, there is no solution for x.