A circle is centered at (5,15) and has a radius of sqrt{130} units. Point Q = (x,y) is on the circle, has integer coordinates, and the value of the x-coordinate is twice the value of the y-coordinate. What is the maximum possible value for x?
\((2y-5)^2 + (y-15)^2 = 130\\ 4y^2 - 20y+25 + y^2 - 30y+225 = 130\\ 5y^2 - 50y +120=0\\ y^2 - 10y+24=0\\ (y-6)(y-4) = 0\\ y=6,~4\\ x=12,~8\\ max(x) = 12 \)