I know it has two x-intercepts but I'm not sure how to factor polynomials with degrees greater than 2..
Both real roots are irrational. There is a quartic formula, but I wouldn't bother memorizing it. Newton's method is probably the best "algebraic" way of solving it.
Let . For some initial "guess" , let and, for , . As gets larger, you should approach a root of f(x).