For zero gravitational force acting on the mass m_1 , \\dfrac{GMm_1}{(d-x)^2} = \\dfrac{Gmm_1}{x^2} Here x is distance from moon, M is mass of earth, m is mass of moon and d is the distance between the earth and moon. \\Rightarrow \\dfrac{M}{(d-x)^2} = \\dfrac{m}{x^2} \\Rightarrow \\dfrac{81m}{(d-x)^2} = \\dfrac{m}{x^2} \\Rightarrow \\dfrac{81}{(d-x)^2} = \\dfrac{1}{x^2} \\Rightarrow \\dfrac{(d-x)^2}{81} = x^2 \\Rightarrow \\dfrac{d-x}{9} = x Solving gives: x = \\dfrac{d}{10} = 38,500 km