112=128t^2-16t

Solution for 112=128t^2-16t equation:

112=128t^2-16t

We move all terms to the left:

112-(128t^2-16t)=0

We get rid of parentheses

-128t^2+16t+112=0

a = -128; b = 16; c = +112;
Δ = b2-4ac
Δ = 162-4·(-128)·112
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-240}{2*-128}=\frac{-256}{-256}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+240}{2*-128}=\frac{224}{-256}
=-7/8
$