I am trying to find bifurcation points in 1 dimension, but am having trouble finding critical points of
$x'=\mu x -2x^2-x^3+ \delta$
( where $x$ is my variable, $\mu$ is a parameter, and $\delta$ is a small, positive parameter, called a imperfection parameter in the problem)
I know there is a cubic formula to solve something like this, but it's rather messy to deal with on its own, let alone with symbols. I was wondering if there were any better methods of finding the critical points.