continued fraction of $\sqrt{10k+3}$ Could you please help me to find the continued fraction of 
$$\sqrt{10k+3}.$$
Where $k$ is a positive integer.
All the best,

\begin{equation*}
x+1=\sqrt{10k+3}
\end{equation*}
\begin{equation*}
x^{2}+2x+1=10k+3
\end{equation*}
\begin{equation*}
x^{2}+2x=10k+2
\end{equation*}
\begin{equation*}
x\left(x+2\right)=10k+2
\end{equation*}
\begin{equation*}
x=\dfrac{10k+2}{2+x}
\end{equation*}
\begin{equation*}
x=\dfrac{10k+2}{2+\dfrac{10k+2}{2+\dfrac{10k+2}{2+\dots}}}
\end{equation*}
Then,
\begin{equation*}
\sqrt{10k+3}=1+x
\end{equation*}
\begin{equation*}
\sqrt{10k+3}=1+\dfrac{10k+2}{2+\dfrac{10k+2}{2+\dfrac{10k+2}{2+\dots}}}
\end{equation*}
