To solve this equation, we can cross multiply:

3(4x + 5) = 2(3x - 1)

12x + 15 = 6x - 2

12x - 6x = -2 - 15

6x = -17

x = -17/6

Therefore, the solution to the equation (3x-1)/2 = (4x+5)/3 is x = -17/6.