Y=-16t^2+14t+32

Solution for Y=-16t^2+14t+32 equation:

=-16Y^2+14Y+32

We move all terms to the left:

-(-16Y^2+14Y+32)=0

We get rid of parentheses

16Y^2-14Y-32=0

a = 16; b = -14; c = -32;
Δ = b2-4ac
Δ = -142-4·16·(-32)
Δ = 2244
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:

$\sqrt{\Delta}=\sqrt{2244}=\sqrt{4*561}=\sqrt{4}*\sqrt{561}=2\sqrt{561}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{561}}{2*16}=\frac{14-2\sqrt{561}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{561}}{2*16}=\frac{14+2\sqrt{561}}{32}
$