$$x\%100+x\%(x\%100)+x\%(x\%(x\%100))...=a$$ It repeats $b$ times.
$a$ is known.
$b$ is known.
How to find $x$?
I am not sure I formatted right, so I note that $x\%100$ means $x$ percent of $100$. Let me know, if something is wrong.
Equations are polynomials, examples: $$x=a$$ $$\frac{x^2}{100}+x=a$$ $$\frac{x^4}{1000000}+\frac{x^2}{100}+x=a$$ $$\frac{x^8}{100000000000000}+\frac{x^4}{1000000}+\frac{x^2}{100}+x=a$$ $$\frac{x^{16}}{1000000000000000000000000000000}+\frac{x^8}{100000000000000}+\frac{x^4}{1000000}+\frac{x^2}{100}+x=a$$
In according to Galois Theory, it may have solution formula, quote:
The formulas for the solutions of all look like towers: using square-roots, square-roots of square-roots, or cube-roots of square-roots, and so on upwards.
I need to find $x$ using solution formula, not by numerical methods like checking for each number to get approximate solution.
I note, if $x$ is $50\%$, it is easy to find, example:
$50+25+12.5=85.5$
$100-(87.5)=12.5$
$100-(87.5-12.5)=25$
$100-(87.5-12.5-25)=50$