0=-16t^2+85t-50

Solution for 0=-16t^2+85t-50 equation:

0=-16t^2+85t-50

We move all terms to the left:

0-(-16t^2+85t-50)=0

We add all the numbers together, and all the variables

-(-16t^2+85t-50)=0

We get rid of parentheses

16t^2-85t+50=0

a = 16; b = -85; c = +50;
Δ = b2-4ac
Δ = -852-4·16·50
Δ = 4025
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:

$\sqrt{\Delta}=\sqrt{4025}=\sqrt{25*161}=\sqrt{25}*\sqrt{161}=5\sqrt{161}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-5\sqrt{161}}{2*16}=\frac{85-5\sqrt{161}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+5\sqrt{161}}{2*16}=\frac{85+5\sqrt{161}}{32}
$