\(\Leftrightarrow x\left(3\sqrt{2}+\sqrt{3}\right)=\sqrt{6}+2\sqrt{2}\\ \Leftrightarrow x=\dfrac{\sqrt{6}+2\sqrt{2}}{3\sqrt{2}+\sqrt{3}}=\dfrac{\left(\sqrt{6}+2\sqrt{2}\right)\left(3\sqrt{2}+\sqrt{3}\right)}{15}\\ \Leftrightarrow x=\dfrac{6\sqrt{3}+3\sqrt{2}+12+2\sqrt{6}}{15}\)