Y=-16x^2+64x+6

Solution for Y=-16x^2+64x+6 equation:

=-16Y^2+64Y+6

We move all terms to the left:

-(-16Y^2+64Y+6)=0

We get rid of parentheses

16Y^2-64Y-6=0

a = 16; b = -64; c = -6;
Δ = b2-4ac
Δ = -642-4·16·(-6)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{70}}{2*16}=\frac{64-8\sqrt{70}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{70}}{2*16}=\frac{64+8\sqrt{70}}{32}
$