Y=-16t2+80t+224

Solution for Y=-16t2+80t+224 equation:

=-16Y^2+80Y+224

We move all terms to the left:

-(-16Y^2+80Y+224)=0

We get rid of parentheses

16Y^2-80Y-224=0

a = 16; b = -80; c = -224;
Δ = b2-4ac
Δ = -802-4·16·(-224)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-144}{2*16}=\frac{-64}{32}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+144}{2*16}=\frac{224}{32}
=7
$