$ \sqrt{3x^2-7x+3}-\sqrt{3x^2-5x-1}+\sqrt{x^2-3x+4}-\sqrt{x^2-2}=0$$\Leftrightarrow \frac{3x^2-7x+5-3x^2+5x+1}{\sqrt{3x^2-7x+3}+\sqrt{3x^2-5x-1}}+\frac{x^2-3x+4-x^2+2}{\sqrt{x^2-3x+4}+\sqrt{x^2-2}}=0$
$\Leftrightarrow \frac{-2(x-2)}{\sqrt{3x^2-7x+3}+\sqrt{3x^2-5x-1}}+\frac{-3(x-2)}{\sqrt{x^2-3x+4}+\sqrt{x^2-2}}=0$
$\Leftrightarrow (x-2)(\frac{2}{\sqrt{3x^2-7x+3}+\sqrt{3x^2-5x-1}}+\frac{3}{\sqrt{x^2-3x+4}+\sqrt{x^2-2}})=0$
$\Rightarrow x=2$ (thử lại đúng)
vậy $ \color{blue}{x=2}$