How to find the expression for Vout?
In your lower schema, you are putting a wire between the + and - inputs of the op-amp: This is wrong. There is no \$i_3\$ current, and no current into the op-amp inputs.

Just write down the equations:


\$V_{A+} = \dfrac{V_2 \times R_4}{R_3 + R_4}\$
\$\dfrac{V_1 - V_{A-}}{R_1} = - \dfrac{V_O - V_{A-}} {R_2}\$
\$V_{A+} = V_{A-}\$ (condition for the amplifier to be in linear mode)


Rearrange a bit... et voilà!