Applying the Law of Cosines

This is supposed to be an easy problem that uses the law of cosines, but I must be overlooking something - can someone please give me a hint?

The problem: Point O is located at (0,0). Point A is located at (8,6). Point P (x,10) is moving along the line y = 10. Find the positive value of x when angle OPA is 60 degrees.

So far I have a = OP = [tex]\sqrt{x^2 + 100}[\math]

b = PA = [tex]\sqrt{4^2+(8 - x)^2}[\math]

100 = [tex] a^2 + b^2 - ab [\math]

Unfortunately this gives a 4th degree equation and no graphing calculators are allowed to be used for this problem. Using a graphing calculator I find that x = 5.634. If I use the tangent angle addition formula I also get x = 5.634, but this needs to be solved using the law of cosines. What am I missing here, and why can't I get LaTeX to work?