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

Question

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?

Answer 1

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

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

If you cross multiply them, we get a quadratic equation and we use the quadratic formula.