This is a nice problem, and it's differential; [-GM
em/x^2]-[-GM
mm/(r-x)^2]
However, when you equate this to zero you get an issue! You can never have a value of x for which you divide the constants by to get zero! 1/x can never equal zero!
So your graph shoots off to infinite! The solution looks something like this.. (assuming an 80kg astronaut)
However, that would give a solution of around 6'800km. I'm not convinced your original equation was correct though.
The gravitational pull of something is equal to [GM
object]/r^2, so the point where the 2 attractions balance
[G*M
e]/r^2=[G*M
m]/R^2
Given G and the Masses are constant you could solve for R like that.
This may all be rubbish, but just my ideas. Sorry if this wastes your time!