How to make sense of the math behind differential opamp
An op amp is a very high gain amplifier.  It amplifies the voltage difference between the + and - inputs.  Connecting the output to the - input creates a closed loop negative feedback system, and the net effect is that it will try to drive the voltage difference to zero.
With the voltage difference zero, effectively no current can enter the - terminal.  Any current presented at the - terminal, by e.g. a voltage applied to the input resistor, must flow &quot;around&quot; the op amp, through the feedback resistor.  Vin/Rin = Iin.  Iout x Rout = Vout, and Iout = -Iin, so Av (voltage gain) = -Rout/Rin.
In the circuit at hand, Av = 499/205 = 2.434.  Av in dB = 20 log (Vo/Vi) = 20 log 2.434 = 20 x 0.3863 = 7.723 dB.