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\sqrt{2}x=2\sqrt{3}
Swap sides so that all variable terms are on the left hand side.
\frac{\sqrt{2}x}{\sqrt{2}}=\frac{2\sqrt{3}}{\sqrt{2}}
Divide both sides by \sqrt{2}.
x=\frac{2\sqrt{3}}{\sqrt{2}}
Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.
x=\sqrt{6}
Divide 2\sqrt{3} by \sqrt{2}.