Try the following:
\begin{align*} \frac{\delta \phi}{\delta x_1} = {} &\frac{9}{8}\frac{\delta_1\phi}{\delta_1x_1}-\frac{1}{8}\frac{\delta_3\phi}{\delta_3x_1} \\ & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right]\\ & \mbox{some text in the middle} \\ & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right] \end{align*}
If you have a lot of text, you probably want to use \phantom :
\begin{align*} \frac{\delta \phi}{\delta x_1} = {} &\frac{9}{8}\frac{\delta_1\phi}{\delta_1x_1}-\frac{1}{8}\frac{\delta_3\phi}{\delta_3x_1} \\ & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right] \end{align*} Some text in the middle, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, \begin{align*} \phantom{\frac{\delta \phi}{\delta x_1} = {}} & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right] \end{align*}
If you don't want to use \phantom , the only solution I can come up with is the following:
\usepackage{multirow} .... \begin{document} \[ \begin{array}{rl} \frac{\delta \phi}{\delta x_1} = {} &\frac{9}{8}\frac{\delta_1\phi}{\delta_1x_1}-\frac{1}{8}\frac{\delta_3\phi}{\delta_3x_1} \\ & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right]\\[5mm] \multicolumn{2}{l}{\parbox{\linewidth}{Some text in the middle, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text, more text}}\\[1cm] & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right] \end{array} \] \end{document}
I donβt think there is a direct way to βbindβ the width of one column of one table / eqnarray / align to another.