Have you considered the Quadratic nature of this particular example? If you don't see it, substitute y = x^2 and it should become obvious.
How do you solve for x with a fourth order polynomial?
The problem I'm working with now is asking for the largest possible value of x for the equation 8x^4 - 16x^2 = 4.
I've played around with it some, but can't work out a viable way to solve for x. Any suggestions are appreciated.
May as well start by cancelling 4:
This is equal to . Taking TKHunny's suggestion and saying that then it becomes . That is standard quadratic form which can be solved using your favourite method.
Once you have solutions for y take the square root to get your x values.
edit: This equation doesn't factor, use the quadratic formula or complete the square
edit 2: You'll get four solutions although some may be complex