find the value of k on which the line
(k-3)-(4-k)^2*g+k^2-k+6=0.
Is "equals" the verb in that sentence? It looks like an incomplete question. What is the value of g?
You can solve the quadratic to get the two values of k where f(k),
(k-3)-(4-k)^2*g +k^2 -k +6,
equals zero. It will depend upon g.