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

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

-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}
$