Transfer Function Of Multiple Feedback Bandpass Filter
By nodal analysis, using \$\large\Sigma\$(currents away from node) = 0:

Let \$\small V\$ be the voltage at the \$\small R_1,\: R_2,\: C_3,\: C_4\$ node, then:

\$\large\frac{V-V_E}{R_1}+\frac{V}{R_2}+\frac{V}{Z_3}+\frac{V-V_S}{Z_4}=0\$

And, at the summing junction node:

\$\large\frac{-V}{Z_3}+\frac{-V_S}{R_5}=0\$

Eliminating \$\small V\$:

\$\large\frac{V_S}{V_E}=\frac{-R_2Z_4R_5}{R_1R_2(Z_3+Z_4+R_5)+(R_1+R_2)Z_3Z_4}\$