Y=-16x^2+200x+82

Solution for Y=-16x^2+200x+82 equation:

=-16Y^2+200Y+82

We move all terms to the left:

-(-16Y^2+200Y+82)=0

We get rid of parentheses

16Y^2-200Y-82=0

a = 16; b = -200; c = -82;
Δ = b2-4ac
Δ = -2002-4·16·(-82)
Δ = 45248
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:

$\sqrt{\Delta}=\sqrt{45248}=\sqrt{64*707}=\sqrt{64}*\sqrt{707}=8\sqrt{707}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-8\sqrt{707}}{2*16}=\frac{200-8\sqrt{707}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+8\sqrt{707}}{2*16}=\frac{200+8\sqrt{707}}{32}
$