problem: One root of the equation $5x^2+4x=k$ (for some real $k$) is 2. What is the other?
solution: Rearranging the given equation, we get $5x^2+4x-k=0$. That means that the sum of the roots of the equation is $-4/5$. If one of the roots of the equation is 2, then the other must be $-\frac{4}{5}-2=\boxed{-\frac{14}{5}}$.