\(4x-12y=-19\Leftrightarrow12y=4x+19\Leftrightarrow y=\dfrac{1}{3}x+\dfrac{19}{12}\)

The x-coordinates of the intersection points of the graphs satisfy :

\(x^2-3x+3=\dfrac{1}{3}x+\dfrac{19}{12}\Leftrightarrow x^2-\dfrac{10}{3}x+\dfrac{17}{12}=0\)

Since there are 2 intersection points, we can apply the Vieta's formulas. The answer is \(\dfrac{10}{3}\)