jmc

For a quadratic to have only one solution, the discriminant must be 0. Therefore, we have the equation $20^2-4\cdot a\cdot 7=0$. Solving, we get $400-28a=0$. Therefore, $a=\frac{400}{28}=\frac{100}{7}$. Using the quadratic formula, $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, we get the solution $\frac{-20\pm \sqrt{0}}{2\cdot \frac{100}{7}}=-20\cdot \frac{7}{200}=\boxed{-\frac{7}{10}}$.