0=-16t^2+85t+10

Solution for 0=-16t^2+85t+10 equation:

0=-16t^2+85t+10

We move all terms to the left:

0-(-16t^2+85t+10)=0

We add all the numbers together, and all the variables

-(-16t^2+85t+10)=0

We get rid of parentheses

16t^2-85t-10=0

a = 16; b = -85; c = -10;
Δ = b2-4ac
Δ = -852-4·16·(-10)
Δ = 7865
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:

$\sqrt{\Delta}=\sqrt{7865}=\sqrt{121*65}=\sqrt{121}*\sqrt{65}=11\sqrt{65}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-11\sqrt{65}}{2*16}=\frac{85-11\sqrt{65}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+11\sqrt{65}}{2*16}=\frac{85+11\sqrt{65}}{32}
$