How to get the entire equation to work correctly?

Question

I have written the following equation:

\begin{document}
\documentclass[12pt]{article}
\begin{align}
    \begin{split}
    \bigg \{2\rho-\bigg (2l+n-2-\sqrt{n^2-4l^2+4ln-4n+4}\bigg )\bigg\}
    \bigg \{2\rho-\bigg (2l+n-2+\sqrt{n^2-4l^2+4ln-4n+4}\bigg )\bigg\}\geq 0
    \end{split}
    \end{align}
\end{document}

The lines of the equation are getting out of the margin. I did use split and \\ but when I use it the rest of the part of the document starts behaving abruptly . I start getting spaces in between the sections. Can someone please tell me how to fix it? Do I need to use any package??

Answer 1

Here are a few options.¹

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
The options include \texttt{align}
\begin{align}
    \bigl\{2\rho-\bigl(2\ell+n-2-\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}&\notag\\
    \cdot\bigl\{2\rho-\bigl(2\ell+n-2+\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}&\geq 0
\end{align}
and \texttt{multline}
\begin{multline}
    \bigl\{2\rho-\bigl(2\ell+n-2-\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}\\
    \cdot\bigl\{2\rho-\bigl(2\ell+n-2+\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}\geq 0
\end{multline}
and \texttt{aligned}
\begin{equation}
\begin{aligned}
    \bigl\{2\rho-\bigl(2\ell+n-2-\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}&\\
    \cdot\bigl\{2\rho-\bigl(2\ell+n-2+\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}&\geq 0
\end{aligned}
\end{equation}
and \texttt{split}
\begin{equation}
\begin{split}
    \bigl\{2\rho-\bigl(2\ell+n-2-\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}\\
    \cdot\bigl\{2\rho-\bigl(2\ell+n-2+\sqrt{n^2-4\ell^2+4\ell n-4n+4}\bigr)\bigr\}\geq 0
\end{split}
\end{equation}
\end{document}

In the future, please consider posting compilable examples. \documentclass needs to go before \begin{document} and you forgot to load amsmath.

_{¹I personally do not like options (3) or (4), but this is just an opinion. When you have the first time a page break in an equation you may understand why.}

Answer 2

I suggest a different way to cope with such a long formula: use an abbreviation for the expression under the square root.

\documentclass[12pt]{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
  \begin{aligned}[t]
  &\bigl( 2\rho-(2l+n-2-\sqrt{\Delta}\,) \bigr)
   \bigl( 2\rho-(2l+n-2+\sqrt{\Delta}\,) \bigr)\geq 0
  \\[0.5ex]
  &\Delta=n^2-4l^2+4ln-4n+4
  \end{aligned}
\end{equation}

\end{document}

There is no need to go \bigg: just remember to use \, when the square root is followed by a parenthesis.