Solution:
Given;
[tex]c=-6t^2+90t-156[/tex]The x-intercepts are the points where y=0.
Thus;
[tex]\begin{gathered} -6t^2+90t-156=0 \\ \\ -t^2+15t-26=0 \\ \\ -t^2+2t+13t-26=0 \\ \\ -t(t-2)+13(t-2)=0 \\ \\ t=2,t=13 \\ \end{gathered}[/tex]Hence, the x-intercepts are;
[tex](2,0)\text{ and }(13,0)[/tex]