Originally Posted by

**jcsm** Hi, I am working on an economics paper, and I find that the following first order condition for my variable of interest ($\displaystyle \mu \in [0,1]$):

$\displaystyle \frac{\lambda(1+\mu)}{(1-\mu)}=N-x\frac{(1+\mu)}{\sqrt{\mu}}$

I would ideally like to provide an explicit solution, but unfortunately, this would amount to solving a fourth order polynomial. Is there any transformation I can make to $\displaystyle \mu$. which would allow me to provide a tractable explicit solution for the tranformation of the variable... or am I out of luck?

thanks so much in advance!