解:
$\begin{aligned}25(x - 1)^{2}-\sqrt{81}&=0\\25(x - 1)^{2}-9&=0\\25(x - 1)^{2}&=9\\(x - 1)^{2}&=\frac{9}{25}\\x - 1&=\pm\frac{3}{5}\end{aligned}$
当$x - 1=\frac{3}{5}$时,$x=\frac{3}{5}+1=\frac{8}{5};$当$x - 1=-\frac{3}{5}$时,$x=-\frac{3}{5}+1=\frac{2}{5}。$所以$x=\frac{8}{5}$或$x=\frac{2}{5}。$