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Solve the equation for x: $4\sqrt{3} x^{2} +5x-2\sqrt{3} =0$
Given: The equation, $4\sqrt{3} x^{2} +5x-2\sqrt{3} =0$
To do: To solve the equation for x.
Solution: The given equation,
$4\sqrt{3} x^{2} +5x-2\sqrt{3} =0$
$\Rightarrow 4\sqrt{3} x^{2} +8x-3x-2\sqrt{3} =0$
$\Rightarrow 4x( \sqrt{3}x+2) −\sqrt{3}( \sqrt{3}x+2) =0$
$\Rightarrow ( \sqrt{3}x+2)( 4x−\sqrt{3})=0$
If $( \sqrt{3}x+2)=0$
$\Rightarrow x=-\frac{2}{\sqrt{3}}$
If ( 4x−\sqrt{3})=0
$\Rightarrow x=\frac{\sqrt{3}}{4}$
Therefore, $x=-\frac{2}{\sqrt{3}}, \frac{\sqrt{3}}{4}$
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