$\displaystyle
\begin{array}{l}
solve\;in\;R \\
\\
x^4 - 2x^2 - 400x = 9999 \\
\end{array}
$
Bring everything to one side
$\displaystyle x^4 - 2x^2 - 400x - 9999 = 0$.
Now work out the factors (positive and negative) of $\displaystyle 9999$.
Substitute each of these factors into the polynomial.
By the factor theorem, if any of these factors (call it $\displaystyle a$) makes the polynomial $\displaystyle = 0$, then $\displaystyle x - a$ is a factor.
Solve in R? Do you mean for the real solutions?
Anyway, rearrange;
$\displaystyle x^4 - 2x^2 - 400x - 9999= 0$
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