Answer
$x=\left\{ 4,6 \right\}$
Work Step by Step
The factored form of the given expression, $
\dfrac{x^2}{4}-\dfrac{5}{2}x+6=0
$, is
\begin{array}{}
4\left( \dfrac{x^2}{4}-\dfrac{5}{2}x+6 \right)=(0)4
\\\\
1(x^2)-2(5x)+4(6)=0
\\\\
x^2-10x+24=0
\\\\
(x-6)(x-4)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x-6=0
\\
x=0+6
\\
x=6
,\text{ OR}\\\\
x-4=0
\\
x=0+4
\\
x=4
\end{array}
Hence, $
x=\left\{ 4,6 \right\}
$.
