jmc

This problem is immediate once you know the following fact:

For the equation $a{x}^2+bx+c=0$, the sum of the solutions of the equation is $-b/a$ and the product of the solutions is $c/a$.

In this case, $b=1992$ and $a=1$, so the sum of the solutions is $-b/a=\boxed{-1992}$.