Gravitation Force Question | Tricky!

Hi, I am taking Physics Grade 12 at home, so I get teacher's help for 2 hours once a week. They basically give me booklets to do at home and just simply hand it in. But the negative side to this that it's only 2 hours of help and teachers don't know most of the questions (they're new). And also the books are COMPLETE crap; there is little or no explanation behind the physic's equation and leave you to think about equation yourself. There's more questions that I don't get but here's the 1st question from the booklet.

Homework Statement

The mass of the Moon is 7.35 x 1022kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is cancelled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (center to center) is 3.84 x 105km, calculate where this will occur, relative to Earth.

Homework Equations

$$F_{g}=\frac{Gm_{1}m_{2}}{r^2}$$
MMoon=7.35 x 1022kg
MEarth=5.98 x 1024kg
Gconstant=6.67 x 10-11N x m^2/kg^2

The Attempt at a Solution

I think it must be:
$$\frac{F_{(G)moon}}{F_{(G)earth}}=1$$
and you are trying to figure out r.

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Well, is my solution right?

Hootenanny
Staff Emeritus
$$\frac{GM_e}{d^2}-\frac{GM_m}{(r-d)^2} = 0$$