-16t2+128t-112=t

Solution for -16t2+128t-112=t equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-16t^2+127t-112=0

a = -16; b = 127; c = -112;
Δ = b2-4ac
Δ = 1272-4·(-16)·(-112)
Δ = 8961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(127)-\sqrt{8961}}{2*-16}=\frac{-127-\sqrt{8961}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(127)+\sqrt{8961}}{2*-16}=\frac{-127+\sqrt{8961}}{-32}
$