Y=-16x^2+96x+6

Solution for Y=-16x^2+96x+6 equation:

=-16Y^2+96Y+6

We move all terms to the left:

-(-16Y^2+96Y+6)=0

We get rid of parentheses

16Y^2-96Y-6=0

a = 16; b = -96; c = -6;
Δ = b2-4ac
Δ = -962-4·16·(-6)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-40\sqrt{6}}{2*16}=\frac{96-40\sqrt{6}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+40\sqrt{6}}{2*16}=\frac{96+40\sqrt{6}}{32}
$