## Elementary Algebra

$n=\dfrac{1}{3}$
Squaring both sides of the equation and then using the properties of equality, we obtain: \begin{array}{l}\require{cancel}\left( \sqrt{5n-1} \right)^2=\left( \sqrt{2n} \right)^2 \\\\ 5n-1=2n \\\\ 5n-2n=1 \\\\ 3n=1 \\\\ n=\dfrac{1}{3} .\end{array} Upon checking, $n=\dfrac{1}{3}$ satisfies the original equation.