Multiply through by sqrt(2x+1): 3x+2-(2x+1)=2sqrt(2x+1)
x+1=2sqrt(2x+1)
Square each side: x^2+2x+1=4(2x+1)=8x+4
x^2-6x-3=0; complete the square: x^2-6x+9-(9+3)=0; (x-3)^2=12; x-3=+2sqrt(3), so x=3+2sqrt(3) and 3-2sqrt(3).
We need to substitute both these into the original:
3(3+2sqrt(3))/sqrt(2(3+2sqrt(3))-sqrt(2(3+2sqrt(3))=2 (using a calculator). 3-2sqrt(3) is also a solution.
Thus x=6.4641 and -0.4641 (evaluating 3+2sqrt(3)).