Y=-16x^2+16+480

Solution for Y=-16x^2+16+480 equation:

=-16Y^2+16+480

We move all terms to the left:

-(-16Y^2+16+480)=0

We get rid of parentheses

16Y^2-16-480=0

We add all the numbers together, and all the variables

16Y^2-496=0

a = 16; b = 0; c = -496;
Δ = b2-4ac
Δ = 02-4·16·(-496)
Δ = 31744
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:

$\sqrt{\Delta}=\sqrt{31744}=\sqrt{1024*31}=\sqrt{1024}*\sqrt{31}=32\sqrt{31}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{31}}{2*16}=\frac{0-32\sqrt{31}}{32}
=-\frac{32\sqrt{31}}{32}
=-\sqrt{31}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{31}}{2*16}=\frac{0+32\sqrt{31}}{32}
=\frac{32\sqrt{31}}{32}
=\sqrt{31}
$