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

Given: Quadratic equation: $4\sqrt{3} x^{2} +5x-2\sqrt{3} =0$.

To do: To find the value of x.

Solution:

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

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

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

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

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

If $\left( 4x-\sqrt{3}\right) =0$

$\Rightarrow x=\frac{\sqrt{3}}{4}$

If $\left(\sqrt{3} x+2\right) =0$

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

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