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I am wondering if it is possible to simplify the following equation

$$ \frac{P}{r-g} \left( 1- \frac{(1+r)^n}{(1+g)^n} \right) = a$$

In order to obtain an expression for $g$ such as:

$$ g = \ldots $$

I'm not sure whether there is a closed-form solution for $g$, though knowing that there is not one would be helpful.

Elements
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    For all practical purposes, there is no closed form if $n\ge 4$. Although there is a closed form for $n=2$ and $n=3$, these are not useful. – André Nicolas May 28 '14 at 19:28
  • @AndréNicolas Thanks! Out of curiosity, how can you tell that there is no closed form for $n \geq 4$? – Elements May 28 '14 at 20:24
  • For $n=4$, the equation simplifies to a fairly general degree $5$ equation, and things get worse for bigger $n$. It is a standard famous result that the general quintic has no closed from solution in terms of the familiar functions. – André Nicolas May 28 '14 at 20:45

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