Fit a non-recatngular parabola in R

I'd like to fit the formula below to a non-rectangular parabola in R.

C = (XI+A-√((ϕI+A )^2-4XϕIA))/2X-R

I have several data points that have values for both C and I. I have an estimate for X, A, ϕ, and R. So I'd like to use the estimates with each observation to get the fitted values and standard errors for each of the parameters.

When I look at fitting curves in R, for example in package nls, I don't know how to use my estimates with my observed data points to get predicted points when I don't use a 'standard' non-linear regression.

Any suggestions or tips would be greatly appreciated.