0=20+80t-5t2

Solution for 0=20+80t-5t2 equation:

0=20+80t-5t^2

We move all terms to the left:

0-(20+80t-5t^2)=0

We add all the numbers together, and all the variables

-(20+80t-5t^2)=0

We get rid of parentheses

5t^2-80t-20=0

a = 5; b = -80; c = -20;
Δ = b2-4ac
Δ = -802-4·5·(-20)
Δ = 6800
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:

$\sqrt{\Delta}=\sqrt{6800}=\sqrt{400*17}=\sqrt{400}*\sqrt{17}=20\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{17}}{2*5}=\frac{80-20\sqrt{17}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{17}}{2*5}=\frac{80+20\sqrt{17}}{10}
$