Re: finding the roots..
You've collided with the solution of the cubic algebraic equation. It's proved by Abel, that the roots can be found in radicals with use of complex values.
See Cardano formula in any book, devoted to linear algebra or just write "Cardano formula" in any search system (google,rambler, yandex, etc.)
If problems don't disappear, let me know. I'll write then this formula in the forum (I've not done it now, because it's too long, but if necessary, I'll do it, of course)
With respect.
Dmitrij