Trying to derive equation out of lm317 datasheet

[avogadro]

I was just trying to derive the equation for output voltage of lm317 for fun and I cant get it. Dont know what Im doing wrong. I attached the image of what I was trying to derive. The closest I get is V0 = Vref((R2 + R3)/(R1)) - 10.

[spec]

+ avogadro

Revised schematic with formula for output voltage attached.

[westfw]

In your second picture: R3, D1 (a zener) and C2 essentially form a conventional -1.25 zener voltage regulator, with the -1.25V output at the D1/R3 junction.
R1/R2 and the LM317 are the normal lm317 regulator, with the "adjust" input biased to -1.25V instead of ground. offsetting the normal 1.25V regulation point of the 317.  (which tries to make sure that Vout is "Adjust+1.25V")

[spec]

In your second picture: R3, D1 (a zener) and C2 essentially form a conventional -1.25 zener voltage regulator, with the -1.25V output at the D1/R3 junction.
R1/R2 and the LM317 are the normal lm317 regulator, with the "adjust" input biased to -1.25V instead of ground. offsetting the normal 1.25V regulation point of the 317.  (which tries to make sure that Vout is "Adjust+1.25V")

Yeah, that is right. Just standard stuff, straight from the datasheet.