This should be easy but somehow I can't get it to work.
I have two functions (f and g). Both depend on x and four other parameters (alpha, beta, gamma and delta).
I am interested in the points where
f=g and f'=g'.
I need the value of x and delta in that point (there are two of these points).
I have tried different things. One of them being first equating f=g, and then plugging the outcome one by one in the equality f'=g', but still that doesn't work, especially when I go numerical (I need both the 'big' analytical outcome and the numerical one).
In case necessary, here are my functions:
f[x_] := 1 + \[Alpha] x - \[Beta] x - \[Alpha] \[Beta] x^2
g[x_] := x/(\[Delta] (1 + \[Alpha] x)) - \[Gamma]/\[Delta]