Question on gravitational field

1. The problem statement, all variables and given/known data
Considering only the gravitational fields of the Earth and the Moon, find the distance from the Earth at which a space capsule travelling between the Earth and the Moon is subject to zero gravitational force.

Mass of the Earth = 5.98 x 1024kg
Mass of the Moon = 7.35 x 1022kg
Radius of Moon's orbit = 3.84 x 108m
Radius of the Earth = 6.38 x 106m
Radius of the Moon = 1.74 x 106m

2. Relevant equations

3. The attempt at a solution

Let x be the distance between the centre of earth and the point of zero gravitational field

Gravitational field due to Earth = Gravational field due to Moon
GME/x2 = GMM/(R - x)2
(ME/MM)1/2=x/(R-x)
x = (ME/MM)1/2R/((ME/MM)1/2 +1)
= 3.79 x 108

But the answer provided is 3.46 x 108

Can anyone tell me where I went wrong?

 PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire
 Recognitions: Gold Member Since the symbolic result is correct you must have made an error during the actual calculation of the number.