7.206. $|x-2|^{10 x^{2}-3 x-1}=1$.

7.206. $|x-2|^{10 x^{2}-3 x-1}=1$.
Solution.

Rewrite the equation as $|x-2|^{10 x^{2}-3 x-1}=|x-2|^{0}$. Then we get two cases:

1) $|x-2|=1$, from which $x-2=-1$ or $x-2=1, x_{1}=1, x_{2}=3$;
2) $\left\{\begin{array}{l}0<|x-2| \neq 1, \\ 10 x^{2}-3 x-1=0\end{array} \Leftrightarrow\left\{\begin{array}{l}x \neq 2, \\ x \neq 1, x \neq 3, \\ x_{3}=-\frac{1}{5}, x_{4}=\frac{1}{2} .\end{array}\right.\right.$

Answer: $-\frac{1}{5} ; \frac{1}{2} ; 1 ; 3$