Solving for $x$ for $\frac{20,000}{21,000 + x} - 1 = \frac{-x}{20,000 + \frac{1}{2} (-x)}$

So I was solving some equations and I stumbled upon this problem.

Solving for $x$ for $$\frac{20,000}{21,000 + x} - 1 = \frac{-x}{20,000 + \frac{1}{2} (-x)}$$ I was wondering what's the fastest way to solve for $x$. Or you just have to brute force it?

• Fastest way? Just dump it into a computer algebra system ;) You can do it by hand by cross multiplying and solving the resulting quadratic equation. – orlp Mar 23 '18 at 2:46

$$\frac{20,000}{21,000 + x} - 1 = \frac{-x}{20,000 + \frac{1}{2} (-x)}$$
$$\frac{-1,000-x}{21,000 + x} = \frac{-x}{20,000 + \frac{1}{2} (-x)}$$