On the Diophantine equation $B_{n_1}+B_{n_2}=2^{a_1}+2^{a_2}+2^{a_3}$

In this study we find all solutions of the Diophantine equation $B_{n_1}+B_{n_2}=2^{a_1}+2^{a_2}+2^{a_3}$ in positive integer variables $(n_1,n_2,a_1,a_2,a_3),$ where $B_n$ denotes the $n$-th balancing number.