Answer
$x=4,x=6$
Work Step by Step
We solve the given equation:
$$\begin{align*}
\dfrac{x^2}{4}-\dfrac{5x}{2}+6&=0\quad&&\text{Write the given equation.}\\
x^2-10x+24&=0\quad&&\text{Multiply each term by }4\text{ to clear denominators.}\\
(x-4)(x-6)&=0\quad&&\text{Factor.}\\
x-4=0&\text{ or }x-6=0\quad&&\text{Set each factor equal to }0.\\
x=4&\text{ or }x=6\quad&&\text{Solve the resulting equations.}
\end{align*}$$
The equation has two solutions: $x=4$ and $x=6$.
Check the results by substituting them in the original equation:
$$\begin{align*}
x&=4\\
\dfrac{4^2}{4}-\dfrac{5(4)}{2}+6&\stackrel{?}{=}0\\
4-10+6&\stackrel{?}{=}0\\
0&=0\checkmark\\\\
x&=6\\
\dfrac{6^2}{4}-\dfrac{5(6)}{2}+6&\stackrel{?}{=}0\\
9-15+6&\stackrel{?}{=}0\\
0&=0\checkmark.
\end{align*}$$
Both solutions check the equation.
