Satellites and newtons universal law of gravitation

The planet alpha, whose mass is M, has one moon, beta, of mass 0.01M. the mean distance between the centres of alpha and beta is R.

point Y represents the distance form planet alpha where the magnitude of the net gravitational force is zero what is the distance in terms of R?

please show your working out, thank you!

the gravitational accelerations have to be equal, and opposed.

accelerations are
a = GM/R^2 where

G = gravitation constant,
M = mass of the object
R = distance from center.

let x = distance of zero -g-point from center of planet, then is the distance of zero-g-point
from center of moon (R - x). Set equations for g equal:

GM/x^2 = Gm/(R-x)^2 with m = M/10
GM/x^2 = 1/10*GM/(R-x)^2
1/x^2 = 1/(10(R-x)^2)
x^2 = 10(R - x)^2
x^2 = 10(R^2 - 2Rx + x^2)
x^2 = 10R^2 - 20Rx + 10x^2
9x^2 - 20Rx + 10R^2 = 0
x^2 - 20R/9*x + 10R^2/9 = 0
x = 10R/9 +- √(100R^2/9^2 - 90R^2/9^2)
x = 10R/9 +- √(10R^2/9^2)
x = 10R/9 +- √(10)*R/9
x = R(10/9 - √(10)/9)
x = R*0.76 <--- distance of zero-g-point from planet

check answer:
set M = 1, m = 0.1 and R = 1--> x = 0.76, R - x = 0.24
GM/x^2 = Gm/(R-x)^2
1/0.76^2 = 0.1/(1-0.76)^2
1/0.76^2 = 0.1/0.24^2
1.73 = 1.73 --> true

OG