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I need to solve this equation that stems from a differential equation, though that isn't really important. Here's the equation that needs to be solved for t:

3t+100=4((9t^3+900t^2+30000t)/(3t+100)…

I've tried myself and always seem to hit a dead end. Using a calculator, I know the answer is 100/3(2^2/3-1) or ~19.58, but can't find a way to get to this answer.

I should mention, I would like this in a fully worked solution if possible. The subject does not allow calculators.