Answer
$t=2.846~h$
Work Step by Step
$(N~o~T)(t)=90t^2+60t+600~~$
$1500=90t^2+60t+600~~$
$0=90t^2+60t-900~~$ (Divide both sides by 30)
$0=3t^2+2t-30~~$ ($a=3,b=2,c=-30$):
$t=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-2±\sqrt {2^2-4(3)(-30)}}{2(3)}=\frac{-2±\sqrt {364}}{6}$
Since $0\leq t\leq6$
$t=\frac{-2+\sqrt {364}}{6}\approx2.846$
