96+80t-16t^2=t

Solution for 96+80t-16t^2=t equation:

96+80t-16t^2=t

We move all terms to the left:

96+80t-16t^2-(t)=0

We add all the numbers together, and all the variables

-16t^2+79t+96=0

a = -16; b = 79; c = +96;
Δ = b2-4ac
Δ = 792-4·(-16)·96
Δ = 12385
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{-(79)-\sqrt{12385}}{2*-16}=\frac{-79-\sqrt{12385}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+\sqrt{12385}}{2*-16}=\frac{-79+\sqrt{12385}}{-32}
$