Electrostats JEE mains

The equations are:

$0 = \frac{q_{1}}{x-4} - \frac{12}{4}$

$0 = \frac{q_{1}}{x + 7} - \frac{12}{7}$

where $x$ is the distance between the two charges.

Solving the two equations, we have $q_{1} = \boxed{44 \mu C}$