Question

Solve the following quadratic equation for $x$: $4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

Answer 1

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

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

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

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

If $\sqrt{3}x+2=0$, then $x=-\frac{2}{\sqrt{3}}$

If $4x-\sqrt{3}=0$, then $x=\frac{\sqrt{3}}{4}$