For a non inverting action, a simple way to obtain it is to keep the feedback loop in place and connecting the terminal where the input used to be connected, to ground, while feeding the input signal to the non inverting input.
This makes the opamp create an output voltage so that the current flowing through the feedback resistor network will be the necessary to develop a voltage at the inverting input that is the same as the non inverting input.
Since we know that the inputs draw virtually no current, then the voltage at the inverting terminal will be defined by the voltage divider created with by the feedback network.
Vinv = VoutR2 / (R1 + R2)
Since Vinv, the inverting input, is at the same potential as the non inverting input, then
Vin = VoutR2/(R1+R2)
The gain is the ratio of output voltage to input voltage
gain = Vout/Vin
A rewrite of the Vin equation gives you
Vin/Vout = R2/(R1+R2)
This las equation is the inverse of what we need, so lets get it straight
Vin = Vout R2/(R1+R2)
Vin (R1+R2) = Vout R2
(R1+R2) = R2 (Vout/Vin)
(R1+R2)/R2 = Vout/Vin
That's an equation for gain, which can be further simplified by separating the terms
(R1/R2) + (R2/R2) = Vout/Vin
(R1/R2) + 1 = Vout/Vin
As you can see, the gain is similar to the inverting amplifier, set by the ratio of the feedback resistors. In this case however, the gain will always be higher than 1. You can think of it as if the amplifier is adding the amplified signal to the non inverting reference voltage, which in fact is the same as the inverting, just that in this case the reference is not ground (0v).
