It's very hard to read your expression, but it looks like it has the form

A x + B x^(-1/2), where (A,B) are independent of x.

If so, you want to solve 2 A - B x^(-3/2) = 0 and the answer is x = (2 A/B)^(-2/3).

If I'm wrong about the form, please substitute numerical example values for everything in your equation except x and re-post it.

p.s. I'm not a Wolfram|Alpha user, but typing "solve 2 A - B x^(-3/2) = 0 for x" worked fine. It you want to do things like collecting all the terms in your expression into A and B, that is easily done in Mathematica, but perhaps not in Wolfram|Alpha. Perhaps you should pick up a trial or home copy of Mathematica for that.