The equation is $$KQ-Kq = nq^n$$ K is known and is a constant. Q will be the independent variable if I can solve for q. n is unknown, but may be considered as a constant and $n\in \mathbb{N}$. I would like to solve for q so I can calculate q as a function of Q for a given n.
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1You have an $n$th-degree polynomial equation in $q$. If $n=2$ it's rather easy, but for higher $n$ it gets unwieldy, and indeed finding an exact closed form for $q$ is impossible if $n>4$. I would use numerical root-finding techniques here. – Parcly Taxel Sep 28 '16 at 15:49
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@ PT: I was afraid of that. Thank you for the explanation and suggestion. – apo Sep 28 '16 at 19:48