You may want to review solving quadratic equations in x3 first.
If you have x4 in place of x3, there's yet another twist. As before, we can only deal with real solutions; but now that means that, if the Quadratic Formula gives us a negative answer, we throw it out, since negative numbers don't have real fourth roots. Each positive number we get from the Quadratic Formula will give us 2 real fourth roots, one positive ad one negative. (Of course, 0 has just one fourth root, 0.)