We know that the line is tangent at the point (2,8)
The derivative of the function at x=2 is

So, the tangent line passes through the point (2,8) and has slope 2. The equation is

This line crosses the x axis where y=0:

3(x+6)>8-(x-7)
3x+18>8-x+7
2x+18>15
2x>-3
X>-3/2