Here is the question: A rectangular prism has a volume of $720$ cm$^3$ and a surface area of $666$ cm$^2$. If the lengths of all its edges are integers, what is the length of the longest edge?
This is from a previously timed competition. Quick answers will be the most helpful.
You can set up equations and use Vieta's formulas to get $x^3+bx^2+333x-720$. How do I solve the problem after this?