2x - 3x^(-1/2) + 1 = 0

I know that when x = 1 that y or the function = 0 but I did not figure that out by myself and needed wolfram alpha to tell me. If I were to do it myself, I would have to plug in numbers which is obviously inefficient.

My question is how do I solve it algebraically? What are the steps? I can't factor out x because there is a +1 and I can't move it to the other side because then it's no longer 0 and therefore no longer easy to figure out the values of x.

Any help would be GREATLY appreciated!

Thanks in advance!