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\sqrt{13x}=6\sqrt{13}
Swap sides so that all variable terms are on the left hand side.
13x=468
Square both sides of the equation.
\frac{13x}{13}=\frac{468}{13}
Divide both sides by 13.
x=\frac{468}{13}
Dividing by 13 undoes the multiplication by 13.
x=36
Divide 468 by 13.