Question:
$3 \sqrt{7} x^{2}+4 x-\sqrt{7}=0$
Solution:
Given:
$3 \sqrt{7} x^{2}+4 x-\sqrt{7}=0$
$\Rightarrow 3 \sqrt{7} x^{2}+7 x-3 x-\sqrt{7}=0$
$\Rightarrow \sqrt{7} x(3 x+\sqrt{7})-1(3 x+\sqrt{7})=0$
$\Rightarrow(3 x+\sqrt{7})(\sqrt{7} x-1)=0$
$\Rightarrow 3 x+\sqrt{7}=0$ or $\sqrt{7} x-1=0$
$\Rightarrow x=\frac{-\sqrt{7}}{3}$ or $x=\frac{1}{\sqrt{7}}=\frac{1 \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}}=\frac{\sqrt{7}}{7}$
Hence, the roots of the equation are $\frac{-\sqrt{7}}{3}$ and $\frac{\sqrt{7}}{7}$.
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