Finding calibration constants via chi square fitting

Dear ROOT experts

I am trying to get the calibration constants by fitting the experimental channel number against the energy values for a BC501 neutron detector. The calibration equation which I am using is Energy(keV) = a*(channel No)^2 + b*(channel No) + c. So first is it possible to do so with minuit fitting function, by defining the chi square between the two spectra ???

If it so then I do not know how do I proceed in the fitting function ???, as I only want to modify the X axis without touching the Y axis (bin contents) values.

The blue one is in experimental spectra (in terms of channel no.) and the red one is the simulated (in terms of energy), the blue is overlay on red. I have put nearly equal contents of the two histograms with experimental spectra having 4096 bins and simulated spectra having 6000 bins.

Any advise will be greatly appreciated…