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Try using implicit_plot so you don't have to solve the equation for y in terms of x.

f = lambda x,y:y^2-3*x-5*y+7
p1=implicit_plot(f, (-4, 4), (-2, 6))
p2= point((1/4, 5/2), size = 45, color='red')

This will do it... you can add your own features.