To solve the equation \( 85x = -10 \), you need to isolate \( x \) on one side of the equation. To do this, divide both sides by 85:
\[ x = \frac{-10}{85} \]
Now, simplify the fraction:
\[ x = \frac{-10 \div 5}{85 \div 5} = \frac{-2}{17} \]
Thus, the solution of the equation \( 85x = -10 \) is:
\[ x = -\frac{2}{17} \]