Somewhat convoluted algebra problem

[gfd43tg]

Ignoring the context of the problem, essentially I am just trying to solve for R1. I am getting frustrated that I am not getting the right answer, so I am wondering where I went wrong in my algebra. The only thing I can guess is that if the left hand side of the equation is a sum, in the step where I square both sides of the equation, I can't square each of the terms on the left separately.

here is the wolfram alpha calculation

http://www.wolframalpha.com/input/?i=0.5*%28%281%2F%286000*1*10^-9%29%2B1%2F%28x*1*10^-9%29%2B%289000%2F18*10^-3%29%29%29+%3D+sqrt%281%2F%2818*10^-3*1*10^-9%29%289%2F6%2B9000%2Fx%2B1%29%29

somewhat embarrassing, I just haven't done this type of mathematical manipulation in a while to remember :(

 

[gfd43tg]

Nevermind, I had to relearn that you do have to square the sum, not the individual terms T.T