The height ‘h’ at which the weight of a body will be the same as that of at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected):

g at height  h=GMeRe+h2g at depth  d=GMeRe21−dReFor Weight to be equal  GMeRe21+hRe2=GMeRe21−dReGiven d = h  ⇒1=1+hRe21−hRe​⇒h2+hR−R2=0   ​comparing with ax2+bx+c=0a=1,b=R and c=−R2​x=−b±b2−4ac2a​h=−R±R2−41−R221h=−R±R2+4R22​⇒h=5R−R2