0=-16t^2+84t+72

Solution for 0=-16t^2+84t+72 equation:

0=-16t^2+84t+72

We move all terms to the left:

0-(-16t^2+84t+72)=0

We add all the numbers together, and all the variables

-(-16t^2+84t+72)=0

We get rid of parentheses

16t^2-84t-72=0

a = 16; b = -84; c = -72;
Δ = b2-4ac
Δ = -842-4·16·(-72)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-108}{2*16}=\frac{-24}{32}
=-3/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+108}{2*16}=\frac{192}{32}
=6
$