How can I solve this equation for $L$. Everything else is known number: $$KL^{2C} - LC^{2C} = (B-C)C^{2C} - C^{2C}(T+KG^2) - KP^2$$
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1Well, what is $C$? if $C=1$ this is just a quadratic equation in $L$. If $C$ is a large integer then this is a hard polynomial to solve. But maybe $C$ isn't even a positive integer? – lulu Jul 30 '18 at 20:32
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1I think you are out of luck unless $2C$ is $1$ or $2$ or $3$ or $4$. Numerical methods may work when that's not the case. – Ethan Bolker Jul 30 '18 at 20:32
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If $K = 0$ this is a line equation in $L$, so let's assume $K \ne 0$. Let's also assume $C$ is a non-negative integer.
Then you are looking at $$L^{2C} - aL -b = 0$$ and for $C>2$ you will not necessarily have analytic solutions.
For $C=0$, it is also linear in $L$. For $C=1$, the quadratic formula applies, and for $C=2$, you have to solve a 4-degree equation, for which you can find closed analytic formulae akin to the quadratic formula...
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