80=16t^2+96t

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

80=16t^2+96t

We move all terms to the left:

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

We get rid of parentheses

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

a = -16; b = -96; c = +80;
Δ = b2-4ac
Δ = -962-4·(-16)·80
Δ = 14336
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:

$\sqrt{\Delta}=\sqrt{14336}=\sqrt{1024*14}=\sqrt{1024}*\sqrt{14}=32\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-32\sqrt{14}}{2*-16}=\frac{96-32\sqrt{14}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+32\sqrt{14}}{2*-16}=\frac{96+32\sqrt{14}}{-32}
$