Question

$\sqrt{3}x( \sqrt{6}x-1)+ \sqrt{2}= 3\sqrt{2}x(x-1)+2 \sqrt{3}$

Answer 1

         
$\sqrt{3}x( \sqrt{6}x-1)+ \sqrt{2}= 3\sqrt{2}x(x-1)+2 \sqrt{3} \\ \sqrt{3}\sqrt{6}x^{2}-\sqrt{3}x+ \sqrt{2}= 3\sqrt{2}x^{2}-3\sqrt{2}x+2 \sqrt{3} \\ 3\sqrt{2}x^{2}-\sqrt{3}x+ \sqrt{2}= 3\sqrt{2}x^{2}-3\sqrt{2}x+2 \sqrt{3} \\ 3\sqrt{2}x^{2}-3\sqrt{2}x^{2}-\sqrt{3}x+3\sqrt{2}x=2 \sqrt{3}-\sqrt{2} \\ 3\sqrt{2}x-\sqrt{3}x= 2\sqrt{3}-\sqrt{2} \\ (3\sqrt{2}-\sqrt{3})x= 2\sqrt{3}-\sqrt{2} \\ \\ x= \frac{2\sqrt{3}-\sqrt{2}}{3\sqrt{2}-\sqrt{3}}$