0=-16t^2+84t+112

Solution for 0=-16t^2+84t+112 equation:

0=-16t^2+84t+112

We move all terms to the left:

0-(-16t^2+84t+112)=0

We add all the numbers together, and all the variables

-(-16t^2+84t+112)=0

We get rid of parentheses

16t^2-84t-112=0

a = 16; b = -84; c = -112;
Δ = b2-4ac
Δ = -842-4·16·(-112)
Δ = 14224
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:

$\sqrt{\Delta}=\sqrt{14224}=\sqrt{16*889}=\sqrt{16}*\sqrt{889}=4\sqrt{889}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{889}}{2*16}=\frac{84-4\sqrt{889}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{889}}{2*16}=\frac{84+4\sqrt{889}}{32}
$