Hi Soroban, thanks very much for your response.
Sorry I'm not really a maths guy hence the strangely written problem.
I think your answer was the one I was looking for but I was trying to solve for X at the end not K.
1+14(K+1)+12(1+2+3....+K)=X
And I think by your result I can see
6k^2+20K+15=X
which is awesome! That's what I was looking for thanks!