Part 2 of mathematical modeling question

[shadedude123]

Okay so after tearing my face off trying to find a 2-cycle, I've managed to make significant process. I divided an enormous polynomial with another polynomial and got a god awful mess which incidentally was correct. Now I'm having trouble solving this equation with x in terms of c:

-3x³-3((c²+8)^.5-c)x²+(6c²+6c((c²+8)^.5-8)x-8c-8((c²+8)^.5)

There are 3 solutions but I have no idea how to reach them:
http://www.wolframalpha.com/input/?...6c(c^2+8)^.5-8)x-8c-8((c^2+8)^.5)+solve+for+x

 

[Office_Shredder]

wolfram alpha probably used the cubic polynomial solving formula and reduced it massively via algebra

 

[shadedude123]

ah, yes. I'll try to look that up.