Mass of a potential black hole in a binary system
Your first equation is incorrect. The left side has dimensions of mass, the right side has dimensions of mass&nbsp;&times;&nbsp;time&nbsp;&times;&nbsp;length-1. The velocity semi-amplitude (usually denoted $K$ rather than $v$) should be raised to the third power.

As noted by @PM-2Ring in the comments, your second equation is also incorrect as you didn't expand the $(m+M)^2$ term correctly.