Y=-16x^2+64x+200

Solution for Y=-16x^2+64x+200 equation:

=-16Y^2+64Y+200

We move all terms to the left:

-(-16Y^2+64Y+200)=0

We get rid of parentheses

16Y^2-64Y-200=0

a = 16; b = -64; c = -200;
Δ = b2-4ac
Δ = -642-4·16·(-200)
Δ = 16896
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:

$\sqrt{\Delta}=\sqrt{16896}=\sqrt{256*66}=\sqrt{256}*\sqrt{66}=16\sqrt{66}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{66}}{2*16}=\frac{64-16\sqrt{66}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{66}}{2*16}=\frac{64+16\sqrt{66}}{32}
$