Question 872608
Discriminant is 144, so p=0 for {{{t=(24-sqrt(144))/2}}} and {{{(24+sqrt(144))/2}}};
or for t=6 and at t=18.


The function has a minimum, so the zeros are the boundaries for {{{p<0}}}.
Profit occurs for {{{0<t<6}}} and for {{{18<t}}}.



{{{graph(300,300,-3,25,-10,160,x^2-24x+108)}}}


Assumption is that {{{t<0}}} has no practical meaning.