Gravitational force moon problem

[Demonsthenes]

Homework Statement

There exists a distance x between the Earth and the moon where the net gravitational force acting on an arbitrary particle of mass m is zero. Assuming only earth-moon interaction, show the distance is given by:

Homework Equations

x = dem/(sqrt(Mm/Me) + 1)

where dem = earth-moon separation distance
x is measured from Earth's center
Mm and e are the masses of the moon and earth

The Attempt at a Solution

I didn't even know where to start here.

 

[cristo]

You should start by looking at the formula that gives the gravitational force between two bodies.