Maruf, Sanjay and Niloy were asked to solve an equation which name is given New Year Equation. Maruf found the roots $2$ and $6$ of the equation by writing the coefficient of x incorrectly. Sanjay found the roots $2$ and $-9$ by writing the constant term incorrectly . Niloy found the exact roots of the equation. So, what is the value of $2a+107b+106c$ if the equation that Niloy derived is expressed as $ax^2+bx+c=0?$