0=-16t^2+84t+216

Solution for 0=-16t^2+84t+216 equation:

0=-16t^2+84t+216

We move all terms to the left:

0-(-16t^2+84t+216)=0

We add all the numbers together, and all the variables

-(-16t^2+84t+216)=0

We get rid of parentheses

16t^2-84t-216=0

a = 16; b = -84; c = -216;
Δ = b2-4ac
Δ = -842-4·16·(-216)
Δ = 20880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20880}=\sqrt{144*145}=\sqrt{144}*\sqrt{145}=12\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{145}}{2*16}=\frac{84-12\sqrt{145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{145}}{2*16}=\frac{84+12\sqrt{145}}{32}
$