On the way to the moon, the Apollo astronauts reach a point where the Moon’s gravitational pull is stronger than that of Earth’s.

Question

Find the distance of this point from the
center of the Earth. The masses of the
Earth and the Moon are 5.98 × 1024 kg and
7.36 × 1022 kg, respectively, and the distance
from the Earth to the Moon is 3.84 × 108 m.
Answer in units of m

Answer 1

at the point, the gravitational attraction of the Earth and the Moon are equal

5.95E24 / d^2 = 7.36E22 / (3.84E8 - d)^2

(3.84E8 - d)^2 = (7.36E22 / 5.95E24) d^2

expand the binomial, and use the quadratic formula to find d

Answer 2

It seems to me to just take the sqrt of each side..
(3.84E8 - d)^2 = (7.36E22 / 5.95E24) d^2
(3.84E8 - d) =d *sqrt (7.36E22 / 5.95E24) =d *k
then
d(k+1)=3.84E8
d= ....