jmc

Note that since we can only use positive integers for $x$, the minimum will be x = 1. Testing x = 2, we get $2^2+4\cdot 2+4=16$. Since $3^2-2^2=5$, we know that only $x=1,2$ will work, thus, there are $\boxed{2}$ positive integer values of $x$ such that this function is less than 20.