Posted by hussain on Friday, May 4, 2012 at 2:12am.
Assuming you meant masses M and m, then we need at distance d from M,
M/d^2 + m/(r-d)^2 = 0
M(r-d)^2 + md^2 = 0
(M+m)d^2 - 2Mrd + Mr^2 = 0
d = r/2 * (M+√Mm)/(M+m)
just as a sanity check, it's easy to see that d=r/2 when M=m
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