So far so good with the first one. The problem with cubics is that it is generally hard to factor them.

The rational root theorem says that the possible rational roots of this equation are . Subbing them in we find that neither of them are roots. So there are no rational roots to this equation. The best we can do from here is numeric approximation. (Well, there's Cardano's method, but it's butt-ugly!) I get 0.453398 is the only real root.

For

we are in a similar situation.

I believe there is a way to use the Lambert W function to solve this, but again we are stuck with numerical approximation. I get x = 1.31907 as the only solution.

-Dan