Short-Answer Questions

$4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0$

$\Rightarrow 4 \sqrt{3} x^{2}+8 x-3 x-2 \sqrt{3}=0$

$\Rightarrow 4 x(\sqrt{3} x+2)-\sqrt{3}(\sqrt{3} x+2)=0$

$\Rightarrow(\sqrt{3} x+2)(4 x-\sqrt{3})=0$

$\Rightarrow \sqrt{3} x+2=0$ or $4 x-\sqrt{3}=0$

$\Rightarrow x=-\frac{2}{\sqrt{3}}=-\frac{2 \sqrt{3}}{3}$ or $x=\frac{\sqrt{3}}{4}$

Hence, $-\frac{2 \sqrt{3}}{3}$ and $\frac{\sqrt{3}}{4}$ are the roots of the given equation.