The mass of the Moon is 81 times less than the mass of the Earth, and the distance between the centers

The mass of the Moon is 81 times less than the mass of the Earth, and the distance between the centers of the Earth and the Moon is 380 thousand km. At what distance from the center of the Moon is the spacecraft located if the forces of attraction of the Moon and the Earth acting on it compensate each other?

Given:
Ms / Ml = 81;
L = 380,000 km;
Fz = Fl;
ll =?

The force of attraction of a planet at a distance from it is determined by the expression:
F = G * M * m / L², where G -, M is the mass of the planet, m is the mass of the body, R is the distance from the center of the planet to the body.
Earth’s gravity:
Fz = G * Mz * m / Lz².
Moon’s gravity:
Fl = G * Ml * m / Ll².
L = Lz + Ll.
Let’s equate the forces of attraction of the planets:
Fz = Fl;
G * Ms * m / Ls² = G * Ml * m / Ls², we will shorten:
Ms / Ls² = Ms / Ls².
Let’s rearrange the masses and distances:
Mz / Ml = Lz² / Ll².
It turns out:
Ls² / Ll² = 81.
Take the square root of both sides:
Ls / Ll = 9.
Then:
Ls = Ls * 9, and from the expression L = Ls + Ls, we express Ls:
Lz = L-Ll.
Substitute in the previous expression:
L-Ll = Ll * 9.
L = Ll * 9 + Ll = 10 * Ll.
Hence:
Ll = L / 10 = 380,000 / 10 = 38,000 km.
Answer: at a distance of 38,000 km.