To solve this expression, we need to follow the order of operations (PEMDAS):

Step 1: Convert all mixed numbers to improper fractions

4 2/7 = (4 7 + 2) / 7 = 30/7
1 3/4 = (1 4 + 3) / 4 = 7/4
3 9/25 = (3 25 + 9) / 25 = 84/25
1 1/2 = (1 2 + 1) / 2 = 3/2

Step 2: Perform the operations

30/7 7/4 - 84/25 : 4/5 + 3/2
= (30/7 7/4) - (84/25 : 4/5) + 3/2
= (30 7)/(7 4) - (84/25 * 5/4) + 3/2
= 30/4 - (420/100) + 150/100
= 7.5 - 4.2 + 1.5
= 4.8

Therefore, the final answer is 4.8.