How to find the inverse of $y=x^3-5x^2+3x+c$ I know how to find the inverse of $y = x^3$, but once you add/subtract another term, that is where I become lost. 
I have used wolframalpha to get an answer. 

I am lost upon how this was obtained.  

This is trivial! All you need to do is find the formula for roots of cubic! First thing you can do is substitute $x=t+\frac{5}{3}$ to remove the second degree term to get $y = t^3-\frac{13}{3}t-\frac{115}{27}$.
For history and proofs, check
http://en.wikipedia.org/wiki/Cubic_function#General_formula_of_roots
