\[8\frac{9^{\backslash 3}}{10} - x = 4\frac{5^{\backslash 5}}{6}\]
\[x = 8\frac{9 \cdot 3}{30} - 4\frac{5 \cdot 5}{30}\]
\[x = 8\frac{27}{30} - 4\frac{25}{30}\]
\[x = 4\frac{2}{30}\]
\[x = 4\frac{1}{15}.\]