How to indent equations?

Try something like

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{equation}
\begin{split}
  A ={} & B + C + D + E + F + \\
        & G + H + I + \dots, \quad\text{while $x$ is true}.
\end{split}
\end{equation}
\end{document} 

Output

If you don't want the equation to be numbered use equation* instead of equation.

As Svend suggested in the comment, in this case it is probably better using \dotsb instead of \dots.

You can use the align environment if you want. Remove the * to get the numbered equation form. The following is MWE:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
A {}={} & B + C + D + E + F +\\
        & G + H + I + \dotsb, \quad \text{while $x$ is true.}
\end{align*}
\end{document}

Another flavor would be like:

\[
\begin{aligned}
A {}={} & B + C + D + E + F +\\
        & G + H + I + \dotsb, \quad \text{while $x$ is true.}
\end{aligned}
\]

or

\[
\begin{array}{r@{}c@{}l}
A   &{}={}& B + C + D + E + F +\\
    &     & G + H + I + \dotsb, \quad \text{while $x$ is true.}
\end{array}
\]

This does not give any numbered version but keeps the alignment. I recommend you read the amsmath documentation and other math related sources to get acquainted with alignments in equations. For example, here in TeX.SX you can make a quick search and you will see several examples of alignment. For instance if I search alignment in equations I would get lots of examples. (click me)

I will also invite you to read the following links:

1. https://tex.stackexchange.com/a/147149/10898
2. https://tex.stackexchange.com/a/122497/10898