It is impossible to do that without knowing , , , and mean! We might guess that and are the speeds of the two objects but that should be given in the problem.
We might guess that and are the speeds of the two objects but that should be given in the problem.
If $v_1$ and $v_2$ are indeed speeds in the lab frame and $v_1^*$, $v_2^*$ are speeds in the center-of-mass frame, then use the definitions $v_i^*=\frac{dr^*_i}{dt}$, $v_i=\frac{dr_i}{dt}$ and the definition of $R$ to rewrite the left-hand side $m_1v_1^*$.