100=-16t^2+80t+32

Solution for 100=-16t^2+80t+32 equation:

100=-16t^2+80t+32

We move all terms to the left:

100-(-16t^2+80t+32)=0

We get rid of parentheses

16t^2-80t-32+100=0

We add all the numbers together, and all the variables

16t^2-80t+68=0

a = 16; b = -80; c = +68;
Δ = b2-4ac
Δ = -802-4·16·68
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-32\sqrt{2}}{2*16}=\frac{80-32\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+32\sqrt{2}}{2*16}=\frac{80+32\sqrt{2}}{32}
$