Bring everything to one side
.
Now work out the factors (positive and negative) of .
Substitute each of these factors into the polynomial.
By the factor theorem, if any of these factors (call it ) makes the polynomial , then is a factor.
Solve in R? Do you mean for the real solutions?
Anyway, rearrange;
Then, I'll use the factor theorem.
Let f(x) = x^4 - 2x^2 - 400x - 9999
By trial and error, find the values of x that are factors of 9999 that make f(x) = 0. Those are the factors of your equation.
Use long division or inspection to divide f(x) by their factors to get other factors, until you get a quadratic which is more easily factorised.
If it cannot be solved, then the values you got for f(x) = 0 are the only solutions.
EDIT: Woops, too late... I was making sure there were solutions =S