Sallen-Key active bandpass first order filter
Here is the way I would choose for manually derive the transfer function:

Start with the general formula for feedback:
H(s)=Hf/(1/Acl+Hb)
with Hf=Forward function, Hb=backward function (feedback factor) and Acl=closed loop gain of the opamp.

Hf=Vp/V1 for Vout=0 and Hb=Vp/Vout for Vin=0. (Vp=Voltage at pos input).

Acl=(1+R6/R7) (in your case: Acl=+2)


Using this method, you have split the whole task into two parts. Finally, you have to rearrange the function with the aim to get a second-order polynominal in the denominator.