0=-16t^2+125t+20

Solution for 0=-16t^2+125t+20 equation:

0=-16t^2+125t+20

We move all terms to the left:

0-(-16t^2+125t+20)=0

We add all the numbers together, and all the variables

-(-16t^2+125t+20)=0

We get rid of parentheses

16t^2-125t-20=0

a = 16; b = -125; c = -20;
Δ = b2-4ac
Δ = -1252-4·16·(-20)
Δ = 16905
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:

$\sqrt{\Delta}=\sqrt{16905}=\sqrt{49*345}=\sqrt{49}*\sqrt{345}=7\sqrt{345}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-7\sqrt{345}}{2*16}=\frac{125-7\sqrt{345}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+7\sqrt{345}}{2*16}=\frac{125+7\sqrt{345}}{32}
$