Y=-16t^2+20t+9

Solution for Y=-16t^2+20t+9 equation:

=-16Y^2+20Y+9

We move all terms to the left:

-(-16Y^2+20Y+9)=0

We get rid of parentheses

16Y^2-20Y-9=0

a = 16; b = -20; c = -9;
Δ = b2-4ac
Δ = -202-4·16·(-9)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{61}}{2*16}=\frac{20-4\sqrt{61}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{61}}{2*16}=\frac{20+4\sqrt{61}}{32}
$