To solve the equation, we will first cross multiply:

5(3x+1) = 2(2x-3)

15x + 5 = 4x - 6

Next, we will subtract 4x from both sides and subtract 5 from both sides:

15x - 4x = -6 - 5
11x = -11

Finally, we will divide by 11 to solve for x:

x = -11/11
x = -1

Therefore, the solution to the equation (3x+1)/2 = (2x-3)/5 is x = -1.