The gain is 3.6, but the offset needs to be applied to the inverting pin, so when the input voltage is 0V, the output is -9V. The inverting gain is equal to the non-invering gain -1, giving 2.6V.
The inverting input must be connected to a 9/2.6 = 3.4615V source, via a resistor of R
F/2.6.
Here's an example, using a 12V regulated power supply to give the offset voltage. R2 & 3 from a potential divider to get the reference voltage. The output resistance of the potential divider is equal to the values of the resistors in parallel, which is (1k1
-1+2k7
-1)
-1 = 781.6R, R5||R6 = 14k21, which is near enough 15k and 39k/15k = 2.6, for a non-inverting gain of 3.6.
The circuit has a gain accuracy of 0.4% and offset of 33mV.
I can explain my working in more detail, later if required.
0 to 5V to +-9V.asc (1.42 kB - downloaded 11 times.)
EDIT:
Here's my working out.
0 to 5V to +-9V working.asc (1.07 kB - downloaded 7 times.)