Two heavy spheres of masses m1 and m2 are kept at a fixed distance apart. A third particle of mass m is placed at a point where the net gravitational…

Let the distance between $m_1$ and $m_2$ be $d$, and let the point be at distance $x$ from $m_1$. Then the distance from $m_2$ is $(d-x)$. For zero net force, $\frac{G m_1 m}{x^2} = \frac{G m_2 m}{(d-x)^2} \implies \frac{\sqrt{m_1}}{x} = \frac{\sqrt{m_2}}{d-x} \implies x = \frac{d \sqrt{m_1}}{\sqrt{m_1} + \sqrt{m_2}}$.