It is given that

${\overrightarrow{F}}_A+{\overrightarrow{F}}_B+{\overrightarrow{F}}_D=0$

Where${\overrightarrow{F}}_A$ ,${\overrightarrow{F}}_B$ and ${\overrightarrow{F}}_D$  are the forces applied by charges placed at A, B and D on the charge placed at C.

$\Rightarrow {\overrightarrow{F}}_B+{\overrightarrow{F}}_D=-{\overrightarrow{F}}_A$

$\left|{\overrightarrow{F}}_B+{\overrightarrow{F}}_D\right|=\sqrt{2}\frac{kqQ}{a^2}\&\left|{\overrightarrow{F}}_A\right|=\frac{k{Q}^2}{2a^2}$

$\therefore \sqrt{2}\frac{kqQ}{a^2}=-\frac{k{Q}^2}{2a^2}\Rightarrow \frac{Q}{q}=-2\sqrt{2}$