I might have misunderstood the question, but Based on what you made a=2 and b=0. Can you give them any value you want?
In that case can't you always make a=0, b= (6K 2 +4k)?
So that 6k2+4k is always of the form 6ab+5a+b, where K is any rational number.
eg. for k=1, 6k2+4k=10=6x0x10+5x0+10
Or should I just go back to my lunch