0=16t^2+82t+5

Solution for 0=16t^2+82t+5 equation:

0=16t^2+82t+5

We move all terms to the left:

0-(16t^2+82t+5)=0

We add all the numbers together, and all the variables

-(16t^2+82t+5)=0

We get rid of parentheses

-16t^2-82t-5=0

a = -16; b = -82; c = -5;
Δ = b2-4ac
Δ = -822-4·(-16)·(-5)
Δ = 6404
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:

$\sqrt{\Delta}=\sqrt{6404}=\sqrt{4*1601}=\sqrt{4}*\sqrt{1601}=2\sqrt{1601}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1601}}{2*-16}=\frac{82-2\sqrt{1601}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1601}}{2*-16}=\frac{82+2\sqrt{1601}}{-32}
$