A generalization of the Ramanujan-Nagell equation

We shall show that, for any positive integer $D>0$ and any primes $p_1,p_2$ not dividing $D$, the diophantine equation $x^2+D=2^s{p}_1^k{p}_2^l$ has at most $63$ integer solutions $(x,k,l,s)$ with $x,k,l\ge 0$ and $s\in \{0,2\}$.