Y=-16t^2+80t+6

Solution for Y=-16t^2+80t+6 equation:

=-16Y^2+80Y+6

We move all terms to the left:

-(-16Y^2+80Y+6)=0

We get rid of parentheses

16Y^2-80Y-6=0

a = 16; b = -80; c = -6;
Δ = b2-4ac
Δ = -802-4·16·(-6)
Δ = 6784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6784}=\sqrt{64*106}=\sqrt{64}*\sqrt{106}=8\sqrt{106}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{106}}{2*16}=\frac{80-8\sqrt{106}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{106}}{2*16}=\frac{80+8\sqrt{106}}{32}
$