-112=-16t^2+96t+112

Solution for -112=-16t^2+96t+112 equation:

-112=-16t^2+96t+112

We move all terms to the left:

-112-(-16t^2+96t+112)=0

We get rid of parentheses

16t^2-96t-112-112=0

We add all the numbers together, and all the variables

16t^2-96t-224=0

a = 16; b = -96; c = -224;
Δ = b2-4ac
Δ = -962-4·16·(-224)
Δ = 23552
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:

$\sqrt{\Delta}=\sqrt{23552}=\sqrt{1024*23}=\sqrt{1024}*\sqrt{23}=32\sqrt{23}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-32\sqrt{23}}{2*16}=\frac{96-32\sqrt{23}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+32\sqrt{23}}{2*16}=\frac{96+32\sqrt{23}}{32}
$