## Elementary Algebra

$x=6$
Squaring both sides of the inequality and using the properties of radicals, the solution to the given equation, $\sqrt{5x+6}=6 ,$ is \begin{array}{l}\require{cancel}\left( \sqrt{5x+6} \right)^2=\left( 6 \right)^2 \\\\ 5x+6=36 \\\\ 5x=36-6 \\\\ 5x=30 \\\\ x=\dfrac{30}{5} \\\\ x=6 .\end{array} Upon checking, $x=6$ satisfies the original equation.