To solve this expression, we first need to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Using the given expression:
(13/2) / (7/31) - 28.5 : 6.75 + (20/2) / 3 - 19 * (9/10)

Step 1: Perform division in the parentheses first:
13/2 = 6.5
7/31 = 0.22580... (rounded)
6.5 / 0.22580... ≈ 28.80

Step 2: Perform the division and subtraction from left to right:
28.80 - 28.5 = 0.30
0.30 : 6.75 = 0.0444... (rounded)

Step 3: Perform the multiplication and division from left to right:
20/2 = 10
10 / 3 = 3.3333 (rounded)
19 * 0.9 = 17.1

Step 4: Perform the final subtraction:
3.3333 - 17.1 ≈ -13.7667

Therefore, the final result of the given expression is approximately -13.7667.