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[TEX]\frac{\lambda(1+\mu)}{(1-\mu)}=N-x\frac{(1+\mu)}{\sqrt{\mu}}[/TEX]

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 [TEX]\mu[/TEX]. 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!