Can't check that right now, but iirc biogas production is taking ~28ish EU/t in distillery
it would be better to spin those carrots in centrifuges instead to get methane.
I did not do the math, but 2 centiruges, spinning about 1 carrot per minute (e.g. extremely low input) was energy-positive (little bit). If you put it to constant spinning, it would be much better; also you can put mob drops in there (well meat), which I've used to have in giant quantities.
Got to my PC, math is as follows:
72 mb of methane per carrot,1440 eu; 1000 methane in lv gas turbine = 0.95*45000 eu = 42750 eu
soo (1000/72)*1440 = 20000 eu needed to produce 1 bucket of methane, so 22750 eu as "profit" eu for 1 centrifuge powering 1 turbine.
If you run a forestry farm, this becomes energy neutral, if not energy-negative; so what I did on my base was a small 1x1 steam boiler from RC, feeding into steam turbine, running forestry farm (enough energy for 3x4x4 non-managed farm structure); 3/4 of farm w/ carrots, 1/4 with resin; all carrots go into centrifuges, which feed 1 gas turbine and RC tank. Tank is slowly gaining some methane, which I'm using in my polyethylene-production.