@Jüri Bogatkin, I like your answer and will only enrich it with more "philosophy". I will try to explain not only HOW the circuit is made but WHY it is made in this way.
If you look closely at the two circuits, you will find they are the same 4-input resistor summer + op-amp. The only difference is in the input voltage of the fourth input - in the non-inverting circuit 0 V (ground) is applied to R1 (the ground is the "source") while in the inverting circuit VOUT is applied to R5 (the op-amp output is the source). In other words, the op-amp output voltage has replaced the zero ground voltage at the lower end of R1. What is the point of this?
The output voltage of the humble resistor summing network is undesired since it decreases the input currents and makes them interdependent. So, we have to remove (zero) it... but we need it since this is the output voltage (the sum).
The clever trick is to remove this voltage by equivalent but opposite voltage and use the latter as output voltage. The op-amp does this work. It "observes" the voltage of the summing point and "pulls" it up or down in the opposite direction (like a "tug of war") until zero this voltage. Thus this point is always "virtual ground" and the op-amp output voltage represents its voltage (with an opposite sign).
The op-amp output voltage is always equal to the voltage drop across R5 and compensates it. Figuratively speaking, it acts as a "negative resistor" with resistance -R5. The result is zero resistance... as though the summing point is connected by a piece of wire to ground... but still there is output voltage at the op-amp output...
Finally, let's formulate a "golden rule" for converting a passive summing circuit into an active inverting circuit:
Add another input (resistor).
Supply it with a compensating voltage that neutralizes the output voltage of the passive summing circuit.
Use the compensating voltage as the output voltage.
See also a Wikibooks story about the passive summing circuit and download an interactive Flash movie (exe file with embedded Flash player) about the op-amp inverting summer.