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?

  • $\begingroup$ 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. $\endgroup$ – orlp Mar 23 '18 at 2:46

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

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

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


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