Answer
$x=9$
Work Step by Step
Using the properties of equality, the given equation, $
2x-5\sqrt{x}=3
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x-3=5\sqrt{x}
.\end{array}
Raising both sides to the second power, then the solution/s to the equation above is/are
\begin{array}{l}\require{cancel}
(2x-3)^2=25x
\\\\
(2x)^2+2(2x)(-3)+(-3)^2=25x
\\\\
4x^2-12x+9=25x
\\\\
4x^2+(-12x-25x)+9=0
\\\\
4x^2-27x+9=0
\\\\
(4x-1)(x-9)=0
\\\\
x=\left\{ \dfrac{1}{4}, 9 \right\}
.\end{array}
Upon checking, only $
x=9
$ satisfies the original equation.