Displayed equations you can write only in p{...}
type cells (or X
, if you use \tabularx
). Since your \multicolumn
use `` cell type, you have error. As solution you can use p{\hsize}
in \multicolumn
too:
\documentclass{article}
\usepackage{mathtools}
%---------------------------------------------------------------%
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\begin{document}
\begin{table}
\centering
\begin{tabular}{p{7cm} | p{7cm} }
Equation 1 & Equation 2\\
\hline
\begin{align*}
a^2+b^2 = c^2
\end{align*}
&
\begin{align*}
E=m\cdot c^2
\end{align*}\\ \hline
\multicolumn{2}{p{\hsize}}{
\begin{align*}
R=\dfrac{U}{I}
\end{align*} }\\ \hline
\end{tabular}
\end{table}
\end{document}
however, result is not very promising:

Better is use tabularx
:
\documentclass{article}
\usepackage{mathtools}
\usepackage{tabularx}
\newcolumntype{C}{>{\centering\arraybackslash}X}
%---------------------------------------------------------------%
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\begin{document}
\begin{table}
\centering
\begin{tabularx}{\linewidth}{C | C }
Equation 1 & Equation 2\\
\hline
\begin{align*}
a^2+b^2 = c^2
\end{align*}
&
\begin{align*}
E=m\cdot c^2
\end{align*}\\ \hline
\multicolumn{2}{>{\hsize=2\hsize}C}{
\begin{align*}
R=\dfrac{U}{I}
\end{align*} }\\
\hline
\end{tabularx}
\end{table}
\end{document}

Red lines show page layout (from package showframe
, in real use you should deleted this package in preamble).
Edit:
I wonder, why you use align
environment, if the equation in the cell has only one line ... so maybe it is worth to consider to use the following solution:
\documentclass{article}
\usepackage{mathtools}
\usepackage{makecell, tabularx}% added makecel for gaped cells
\newcolumntype{C}{>{\centering\arraybackslash}X}
\setcellgapes{5pt}% set vertical gapes above and below cells' contents
\begin{document}
\begin{table}
\centering
\makegapedcells% use gaps in cells
\begin{tabularx}{\linewidth}{>{$\displaystyle}C<{$}|>$\displaystyle}C<{$}}% use in line math environment, but with \displaystyle
\text{Equation 1} & \text{Equation 2} \\
\hline
a^2+b^2 = c^2 & E=m\cdot c^2 \\
\hline
\multicolumn{2}{>{\hsize=2\hsize$\displaystyle}C<{$}}{
\begin{aligned}% in case, that you really have multi line and aligned equations
R & =\frac{U}{I} \\
U & =I R
\end{aligned} }\\
\hline
\end{tabularx}
\end{table}
\end{document}
