No, sorry, it’s not the right answer. In fact, there are two solutions for x. But you do have the right idea. If you follow your logic, that is, x/10=1/(20+x), then substitute for x (=10/(20+x) you get:
x=10/(20+10/(20+10/(20+10...
This is not the same as the given equation. Hint: 2x=20/(20/(20/(20...