0=-80t+16t^2+3.5

Solution for 0=-80t+16t^2+3.5 equation:

0=-80t+16t^2+3.5

We move all terms to the left:

0-(-80t+16t^2+3.5)=0

We add all the numbers together, and all the variables

-(-80t+16t^2+3.5)=0

We get rid of parentheses

-16t^2+80t-3.5=0

a = -16; b = 80; c = -3.5;
Δ = b2-4ac
Δ = 802-4·(-16)·(-3.5)
Δ = 6176
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:

$\sqrt{\Delta}=\sqrt{6176}=\sqrt{16*386}=\sqrt{16}*\sqrt{386}=4\sqrt{386}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{386}}{2*-16}=\frac{-80-4\sqrt{386}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{386}}{2*-16}=\frac{-80+4\sqrt{386}}{-32}
$