Y=-16x^2+128x+2

Solution for Y=-16x^2+128x+2 equation:

=-16Y^2+128Y+2

We move all terms to the left:

-(-16Y^2+128Y+2)=0

We get rid of parentheses

16Y^2-128Y-2=0

a = 16; b = -128; c = -2;
Δ = b2-4ac
Δ = -1282-4·16·(-2)
Δ = 16512
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:

$\sqrt{\Delta}=\sqrt{16512}=\sqrt{64*258}=\sqrt{64}*\sqrt{258}=8\sqrt{258}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{258}}{2*16}=\frac{128-8\sqrt{258}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{258}}{2*16}=\frac{128+8\sqrt{258}}{32}
$