To solve this equation, we need to isolate the square root terms on one side of the equation and square both sides to eliminate the square roots.

First, let's start by moving all the square root terms to one side:

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

We can rewrite the equation as:

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

Next, square both sides of the equation to eliminate the square roots:

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

Expand the squared terms on both sides:

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

Simplify the expressions:

9x^2 + 12x + 4 = 3x + 2√(x + 3)√(2x - 1) + 6x + 1 + 6x√(x + 3)(2x - 1) + 2x + 2

Now, we have eliminated the square roots from the equation. Simplify further if possible and solve for x by isolating the terms.