Calculating the Distance of a Zero Gravitational Field Between Earth and Moon

[Nikola]

Homework Statement

There is a point between the Earth and the moon where the total gravitational field is zero. Given that the mass of Earth is 6.0*10^24 kg, the mass of the moon is 7.3*10^22 kg and the radius of the Moon's orbit is 3.8*10^8 m, calculate the distance of this point from the center of the earth.

Homework Equations

If there is always a gravitational field when does the field become negligible? (because it says the gravitational field is zero).

The Attempt at a Solution

i attempted substituting the equation into one another (g=F/m with g=Gm/r^2) but just got an answer that was way off. Maybe i substituted wrong.

 

[haruspex]

If there is always a gravitational field when does the field become negligible?

there are two fields, one from the moon and one from the Earth. In between those fields pull in opposite directions. There must be a point at which they balance. Find that point.

 

[lekh2003]

At what distance $r$ and $3.8*10^8 - r$ does the gravitational field for the Earth and the gravitational field from the moon equal each other (since they are opposite forces)?