$(5$ points$)$ Find $a,b,c$ so that $y=a{x}^2+bx+c$ is a solution of

$Q=a{x}^2+bx+C,\{\begin{array}{c}\frac{d^{2}y}{d{x}^2}-\frac{dy}{dx}+6y=6x^2-2x+26\end{array}$