-16t^2+96t=-112

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

-16t^2+96t=-112

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -16; b = 96; c = +112;
Δ = b2-4ac
Δ = 962-4·(-16)·112
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-128}{2*-16}=\frac{-224}{-32}
=+7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+128}{2*-16}=\frac{32}{-32}
=-1
$