diff --git a/main.tex b/main.tex
index 406c5ca5c3dc2699260fc08c4c6a2ef5da0a93d1..15cbd92e7b0b148f79b100920da898be6db749f8 100644
--- a/main.tex
+++ b/main.tex
@@ -8,6 +8,7 @@
 \usepackage{hyperref}
 \usepackage{color}
 \usepackage{sagetex}
+\usepackage[]{breqn}
 
 \newcommand{\QQ}{\mathbb{Q}}
 \newcommand{\ZZ}{\mathbb{Z}}
@@ -191,6 +192,8 @@ This condition expressed in terms of $R,C,D,r,c,d$ looks as follows:
 	\sage{(0 <= positive_condition.expand() )}
 \end{equation}
 
+
+\noindent
 Expressing $c$ in terms of $m$ as defined in (eqn \ref{eqn-cintermsofm})
 we get the following:
 
@@ -202,6 +205,8 @@ we get the following:
 	\sage{(0 <= positive_condition) + 2*R*d - 4*d*r}
 \end{equation}
 
+
+\noindent
 This can be rearranged to express a bound on $d$ as follows:
 
 \begin{sagesilent}
@@ -211,12 +216,12 @@ This can be rearranged to express a bound on $d$ as follows:
 	nc = nc.subs(r_alt == r - R/2).expand() # resubs r back in
 \end{sagesilent}
 
-\begin{footnotesize}
-\begin{equation}
+\begin{dmath}
 	\sage{nc}
-\end{equation}
-\end{footnotesize}
+\end{dmath}
+
 
+\noindent
 In the case $\beta = \beta_{-}$ (or $\beta_{+}$) this can be simplified.