Looks like you got yourself a *cubic*.
There is a standard algorithmic way of solving this, but it's unwieldy and long-winded (although very pretty).
Your best way of tackling one of these is (assuming you're given one of these as an exercise at elementary level) is seeing whether there's a factor.
That is, given an equation in the form:
(which is effectively what you've got when you rearrange your equation above)
... you want to try and get it in the form:
Any of this familiar? If not, you've got a way to go before you're up to this - you will need to struggle through solving quadratics (which is like cubics but not as bad).