Y=-16t2+486

Solution for Y=-16t2+486 equation:

=-16Y^2+486

We move all terms to the left:

-(-16Y^2+486)=0

We get rid of parentheses

16Y^2-486=0

a = 16; b = 0; c = -486;
Δ = b2-4ac
Δ = 02-4·16·(-486)
Δ = 31104
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:

$\sqrt{\Delta}=\sqrt{31104}=\sqrt{5184*6}=\sqrt{5184}*\sqrt{6}=72\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{6}}{2*16}=\frac{0-72\sqrt{6}}{32}
=-\frac{72\sqrt{6}}{32}
=-\frac{9\sqrt{6}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{6}}{2*16}=\frac{0+72\sqrt{6}}{32}
=\frac{72\sqrt{6}}{32}
=\frac{9\sqrt{6}}{4}
$