Y=-16t^2+8t+9

Solution for Y=-16t^2+8t+9 equation:

=-16Y^2+8Y+9

We move all terms to the left:

-(-16Y^2+8Y+9)=0

We get rid of parentheses

16Y^2-8Y-9=0

a = 16; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·16·(-9)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{10}}{2*16}=\frac{8-8\sqrt{10}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{10}}{2*16}=\frac{8+8\sqrt{10}}{32}
$