Answer
$x= 1$ and $x= 9$
Work Step by Step
Given
\begin{equation}
\begin{aligned}
& 4 \sqrt{x}=x+3 \\
& {[-1,10,1] \text { by }[-1,14,1]}
\end{aligned}
\end{equation}
Let
\begin{equation}
\begin{aligned}
f(x)&= 4 \sqrt{x}\\
g(x)&=x+3\\
\end{aligned}
\end{equation}
The plots of the two functions are shown in the figure. We see that the points of intersection between the graphs of the functions are at $(x,y) = (1,4)$ and at $(x,y) = (9,12)$. This means that the solution is $x= 1$ and $x= 9$ .
Let's check.
\begin{equation}
\begin{aligned}
4 \sqrt{1}&\stackrel{?}{=}1+3 \\
4& =4\checkmark \\
4 \sqrt{9}& \stackrel{?}{=}9+3 \\
4\cdot3& \stackrel{?}{=}12 \\
12& = 12\checkmark
\end{aligned}
\end{equation}
