Y=-16x2+11500

Solution for Y=-16x2+11500 equation:

=-16Y^2+11500

We move all terms to the left:

-(-16Y^2+11500)=0

We get rid of parentheses

16Y^2-11500=0

a = 16; b = 0; c = -11500;
Δ = b2-4ac
Δ = 02-4·16·(-11500)
Δ = 736000
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:

$\sqrt{\Delta}=\sqrt{736000}=\sqrt{6400*115}=\sqrt{6400}*\sqrt{115}=80\sqrt{115}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{115}}{2*16}=\frac{0-80\sqrt{115}}{32}
=-\frac{80\sqrt{115}}{32}
=-\frac{5\sqrt{115}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{115}}{2*16}=\frac{0+80\sqrt{115}}{32}
=\frac{80\sqrt{115}}{32}
=\frac{5\sqrt{115}}{2}
$