How do I produce an equation of mostly text that is not too long for the page?

With delimiters

Another variation with parentheses, using pmatrix of package amsmath.

\documentclass{article}
\usepackage{amsmath}
\usepackage{siunitx}
\DeclareSIUnit{\cells}{cells}
\sisetup{per-mode = symbol}

\begin{document}

\[
  \begin{pmatrix}
    \text{volume of diluted cell suspension}\\
    \text{or number of Petri dishes}
  \end{pmatrix}
  =
  \frac{
    \begin{pmatrix}
      \text{volume of diluted}\\
      \text{cell suspension}
    \end{pmatrix}
    \times
    \begin{pmatrix}
      \text{density of}\\
      \text{undiluted cells}
    \end{pmatrix}
  }{
    \SI[mode=text]{1.7e6}{\cells\per\ml}
  }
\]

\end{document}

Without delimiters

The text blocks can be set with environment matrix of package amsmath. Without visual delimiters I have increased the spacing around the relational operator = (\thickmuskip) and the binary operator + (\medmuskip):

\documentclass{article}
\usepackage{amsmath}
\usepackage{siunitx}
\DeclareSIUnit{\cells}{cells}
\sisetup{per-mode = symbol}

\begin{document}

\[
  \setlength{\thickmuskip}{2\thickmuskip}
  \setlength{\medmuskip}{2\medmuskip}
  \begin{matrix}
    \text{volume of diluted cell suspension}\\
    \text{or number of Petri dishes}
  \end{matrix}
  =
  \frac{
    \begin{matrix}
      \text{volume of diluted}\\
      \text{cell suspension}
    \end{matrix}
    \times
    \begin{matrix}
      \text{density of}\\
      \text{undiluted cells}
    \end{matrix}
  }{
    \SI[mode=text]{1.7e6}{\cells\per\ml}
  }
\]

\end{document}

Variant with tabular

The following uses tabular instead of matrix with decreased space between the lines:

\documentclass{article}
\usepackage{amsmath}
\usepackage{siunitx}
\DeclareSIUnit{\cells}{cells}
\sisetup{per-mode = symbol}

\newcommand*{\textstack}[1]{%
  \text{%
    \renewcommand*{\arraystretch}{.9}%
    \begin{tabular}{@{}c@{}}%
      #1%
    \end{tabular}%
  }%
}

\begin{document}

\[
  \setlength{\thickmuskip}{2\thickmuskip}
  \setlength{\medmuskip}{2\medmuskip}
  \textstack{
    volume of diluted cell suspension\\
    or number of Petri dishes
  }
  =
  \frac{
    \textstack{
      volume of diluted\\
      cell suspension
    }
    \times
    \textstack{
      density of\\
      undiluted cells
    }
  }{ 
    \SI[mode=text]{1.7e6}{\cells\per\ml}
  }
\]

\end{document}

I'd use the smallmatrix-environment and would add brackets around the text to increase readability.

\documentclass{article} 
\usepackage{amsmath}
\begin{document} 
\begin{displaymath}
  \Bigl(\begin{smallmatrix}
          \text{Volume of diluted cell suspension}\\
          \text{ or number of Petri dishes} 
        \end{smallmatrix}\Bigr)
   = \frac{%
        \Bigl(\begin{smallmatrix}
                 \text{Volume of diluted cell suspension}\\
                 \text{or number of Petri dishes} 
              \end{smallmatrix}\Bigr) 
        \times 
        \Bigl(\begin{smallmatrix}
           \text{density of}\\
           \text{undiluted cells} 
          \end{smallmatrix}\Bigr) 
      }
      {1.7\times10^6\,\text{cells}/\text{ml}} 
\end{displaymath}
\end{document}

In the first solution, I tried to preserve the layout that you presented:

\documentclass{article}
\usepackage{stackengine}
\begin{document}  
\small
\stackon{or number of Petri dishes}{Volume of diluted cell suspension}
= \stackunder{%
    \stackunder{volume of undiluted}{cell suspension} $\times$%
    \stackunder{density of undiluted}{cells}%
  }{\stackunder{--------------------------------------------------------}%
               {$1.7\times10^6$ cells/ml}%
  }
\end{document}

Upon reflection, you may desire a slightly different layout. This would probably be better:

\documentclass{article}
\usepackage{stackengine}
\begin{document}
\small
\stackanchor{Volume of diluted cell suspension}{or number of Petri dishes}
= 
\savestack{\num}{%
  \stackanchor{volume of undiluted}{cell suspension} ~$\times$~%
  \stackanchor{density of}{undiluted cells}%
}%
\stackunder{%
  \stackon{-----------------------------------------------------}{\num}%
}{$1.7\times10^6$ cells/ml}%
\end{document}