What you need is a summing amplifier. The 2-input summing amplifier in the link you give is a specific example of the general form, and it may or may not be suitable for your needs.
The general form of the summing amplifier is an invaluable resource in the toolkit of an electronics engineer. The general circuit shown below can be solved using Kirchoff's Current Law and a horrible heap of algebra, but if you're happy to take my word for it, it all boils down to one simple equation and one condition which must be obeyed.
You can have as few or as many plus- and minus-inputs as you like, 3 each are shown here for illustration.
Each input contributes Vn * Rf / Rn to the output, where the Vp/Rp elements are all added to the output, and the Vm/Rm are all subtracted from the output.
There is one strict condition which must be obeyed to allow the math to simplify nicely to this result: the parallel sum of impedances at the inverting input must be precisely equal to the parallel sum of impedances at the non-inverting input. This is where Rc comes in, to balance Rf in the case that all the input resistors are the same value.
If you want to sum two voltages equally, and subtract a quarter of a third, with a circuit which has a 10k feedback resistor, then you want each summing input connected to the non-inverting input with a 10k resistor each, the subtracting input to the inverting input with a 40k resistor and 13k3 resistor from the inverting input to ground to balance the parallel impedances.
In your case, you have an input in the range -0.8V to +1.8V and want to add 0.8V and scale the result to fit the range of your ADC. You don't say what ADC range you need, but as an example I'll choose 5.0V, and assume that you have 5.0V available as a stable analogue reference for the added term.
Your signal input has a range of 2.6V and requires a gain of 5.0/2.6 = 1.92. Without the addition of an offset, the signal would be amplified to produce an output at the ADC of -1.54V to +3.46V. So to the output, you need to add an offset of 1.54V.
Using E24 series values, the gain of 1.92 can be achieved using 7k5/3k9, so Rf = 7k5 and Rp1 = 3k9. The offset of 1.54V can be added by connecting a stable 5.0V reference through Rp2 = 24k. (Vp2 * Rf / Rp2 = 5.0 * 7.5 / 24 = 1.56V which is correct to better than 1.5%). The parallel sum at the inverting input is 7k5 // 24k = 5k7 and the parallel sum at the non-inverting input is simply 10k. So we need to add a 13k3 resistance from the non-inverting input to ground to bring the parallel sum down to 5k7 to match the inverting input. 13k3 can be approximated with two 27k in parallel.
Hope that helps, and gives you a useful tool for future designs.