It is known that many physical systems, both time and space dependent, are described by difference-differential equations. Although the exact solutions to such equations are known to be unique, their determination usually involves a segmented type of solution that is very laborious to obtain. An approximate method of determining any number of roots is described. This approximate procedure allows forward gain and delay to be freely chosen and gives immediately the maximum stable value of forward gain. In many cases, especially where an optimum value of damping constant or forward gain is to be found, it appears that this approximate procedure is more easily applied than any previously described method.