$$\sqrt{3}(x-2)-2x\sqrt{2}=2(x\sqrt{3}-3-x\sqrt{2})$$
$x=2\left(\sqrt{3}-1\right)\approx 1.464101615$
$$\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}=2\left(x\sqrt{3}-3-x\sqrt{2}\right)$$
$$\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}-2\left(x\sqrt{3}-3-x\sqrt{2}\right)=0$$
$$\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}-2x\sqrt{3}+6+2\sqrt{2}x=0$$
$$-\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}+6+2\sqrt{2}x=0$$
$$-\sqrt{3}x-2\sqrt{3}+6=0$$
$$-\sqrt{3}x+6=2\sqrt{3}$$
$$-\sqrt{3}x=2\sqrt{3}-6$$
$$\left(-\sqrt{3}\right)x=2\sqrt{3}-6$$
$$\frac{\left(-\sqrt{3}\right)x}{-\sqrt{3}}=\frac{2\sqrt{3}-6}{-\sqrt{3}}$$
$$x=\frac{2\sqrt{3}-6}{-\sqrt{3}}$$
$$x=2\sqrt{3}-2$$
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