As Vin increases, Vout will increase in accordance with the differential gain. However, as Vout increases, that output voltage is fed back to the inverting input, thereby acting to decrease the voltage differential between inputs, which acts to bring the output down. The circuit will quickly reach a point of stability (known as equilibrium), where the output voltage is just the right amount to maintain the right amount of differential, which in turn produces the right amount of output voltage. Taking the op-amp's output voltage and coupling it to the inverting input is a technique known as NEGATIVE FEEDBACK, and it is the key to having a self-stabilizing system. This stability gives the op-amp the capacity to work in its linear (active) mode, as opposed to merely being saturated fully "on" or "off" as it when used as a comparator, with no feedback at all.
Because the op-amp's gain is so high, the voltage on the inverting input can be maintained almost equal to Vin. Let's say that our op-amp has a differential voltage gain of 200,000. If Vin equals 6 volts, the output voltage will be 6 volts. This creates just enough differential voltage to be manifested at the output terminal, and the system holds there in balance. So for practical calculations, we can assume that the differential voltage between the two input wires is held by negative feedback exactly at 0 volts.
Advantage to using an op-amp with negative feedback is that the actual voltage gain of the op-amp doesn't matter, so long as its very large. In this circuit, the output voltage would still be equal to the non-inverting input voltage
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