Help with ideal op-amp problem
Simple analysis allows you to say that if the voltage output were at point A then the gain at point A is -R2/R1. This has to be true because of the need to keep the voltage at point B equal to zero. Now, if the gain is -R2/R1 at point A it's a simple matter of recognizing that the gain at point "V2" is higher by a certain amount.

That certain amount is also fairly straightforward to see. R2 is virtually grounded therefore it is in parallel with R3 and together they form a potential divider with R4. If the potential divider ratio is G then V2/V1 = -G.R2/R1

I'm looking at your equation and it looks incorrect because if R4 were zero ohms, the formula doesn't reduce to -R2/R1. My formula, using my method is: -

\$\dfrac{V_2}{V_1} = \dfrac{-R_2}{R_1}\cdot \dfrac{R_2 R_3 + R_2 R_4 + R_3 R_4}{R_2 R_3}\$