80=-16t^2+100t+5

Solution for 80=-16t^2+100t+5 equation:

80=-16t^2+100t+5

We move all terms to the left:

80-(-16t^2+100t+5)=0

We get rid of parentheses

16t^2-100t-5+80=0

We add all the numbers together, and all the variables

16t^2-100t+75=0

a = 16; b = -100; c = +75;
Δ = b2-4ac
Δ = -1002-4·16·75
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{13}}{2*16}=\frac{100-20\sqrt{13}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{13}}{2*16}=\frac{100+20\sqrt{13}}{32}
$