To solve this equation, we need to find a common denominator for both fractions:

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

First, we cross multiply to get rid of the fractions:

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

Expand both sides:

2x^2 - 3x + 4x - 6 = 3x^2 - 2x + x - 2

Combine like terms:

2x^2 + x - 6 = 3x^2 - x - 2

Rearrange the equation to set it to zero:

0 = 3x^2 - 2x - 2x^2 + x - 2 + 6

0 = x^2 - x + 4

Now, we will try to factor this quadratic equation. Since it cannot be factored, we can use the quadratic formula to find the values of x:

x = (-(-1) ± √((-1)^2 - 4(1)(4)))/(2(1))

x = (1 ± √(1 - 16))/2

x = (1 ± √(-15))/2

Since we have a negative value under the square root, the solutions are imaginary:

x = (1 ± √15i)/2

Therefore, the solution to the equation is x = (1 ± √15i)/2.