Answer
2.1 seconds
Work Step by Step
$d(t)=-16t^2+30t+6$
$d(t)=0$
$d(t)=-16t^2+30t+6$
$0=-16t^2+30t+6$
$0/-16=(-16t^2+30t+6)/-16$
$0=t^2-15/8t-3/8$
$0+3/8=t^2-15/8t-3/8+3/8$
$3/8=t^2-15/8t$
$3/8+(-15/8*1/2)^2=t^2-15/8t+(-15/8*1/2)^2$
$3/8+(-15/16)^2=t^2-15/8t+(-15/16)^2$
$3/8+(225/256) =t^2-15/8t+225/256$
$3/8+(225/256) =(t-15/16)^2$
$3/8+(225/256) =(t-15/16)^2$
$96/256+(225/256) =(t-15/16)^2$
$321/256 =(t-15/16)^2$
$\sqrt{321/256}=\sqrt {(t-15/16)^2}$
$\sqrt{321}/±16=t-15/16$
We are looking for time, so we can’t have a negative number.
$\sqrt{321}/16=t-15/16$
$\sqrt{321}/16+15/16=t-15/16+15/16$
$(15+\sqrt{321})/16=t$
$(15+17.92)/16=t$
$32.92/16=t$
$t=2.0575$
$t=2.1$ seconds