Y=-16t^2+82t

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

=-16Y^2+82Y

We move all terms to the left:

-(-16Y^2+82Y)=0

We get rid of parentheses

16Y^2-82Y=0

a = 16; b = -82; c = 0;
Δ = b2-4ac
Δ = -822-4·16·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-82}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+82}{2*16}=\frac{164}{32}
=5+1/8
$