Trace of a Parametric Matrix

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Consider the matrix function $T(x)=\begin{pmatrix} 2x+1 & \sqrt{x+4} \\ 3 & \frac{x}{x+2} \end{pmatrix}$ . Find all real values of $x$ that satisfy the following equation for the trace of $T(x)$ :
$(2x+1) + \frac{x}{x+2} = 5$

$x=\frac{-1-\sqrt{65}}{4}$

$x=2$

$x=\frac{-1\pm\sqrt{65}}{4}$

$x=\frac{-1+\sqrt{65}}{4}$

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