Answer
$x=45$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[4]{2x-9}-3=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[4]{2x-9}=3
.\end{array}
Raising both sides of the equation above to the fourth power, then the solution/s is/are
\begin{array}{l}\require{cancel}
2x-9=81
\\\\
2x=81+9
\\\\
2x=90
\\\\
x=\dfrac{90}{2}
\\\\
x=45
.\end{array}
Upon checking, $
x=45
$ satisfies the original equation.