Question 1162485
Set the two equal
0.75x^2-6x+20=2.75x+1.50
0.75x^2-8.75x+18.5=0
x=(1/1.5)(8.75 +/- sqrt (76.56-55.5)); sqrt term is 4.59
the larger root is later in time and is (2/3)(20.22)=8.89 months

(the earlier intersection was at 2.77 months)

can also multiply through by 4 to get 3x^2-35x+74

{{{graph(300,300,-2,10,-10,30,0.75x^2-6x+20,2.75x+1.50)}}}