0=-16t^2+82t+17

Solution for 0=-16t^2+82t+17 equation:

0=-16t^2+82t+17

We move all terms to the left:

0-(-16t^2+82t+17)=0

We add all the numbers together, and all the variables

-(-16t^2+82t+17)=0

We get rid of parentheses

16t^2-82t-17=0

a = 16; b = -82; c = -17;
Δ = b2-4ac
Δ = -822-4·16·(-17)
Δ = 7812
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:

$\sqrt{\Delta}=\sqrt{7812}=\sqrt{36*217}=\sqrt{36}*\sqrt{217}=6\sqrt{217}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-6\sqrt{217}}{2*16}=\frac{82-6\sqrt{217}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+6\sqrt{217}}{2*16}=\frac{82+6\sqrt{217}}{32}
$