Y=-8x^2+16x+2

Solution for Y=-8x^2+16x+2 equation:

=-8Y^2+16Y+2

We move all terms to the left:

-(-8Y^2+16Y+2)=0

We get rid of parentheses

8Y^2-16Y-2=0

a = 8; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·8·(-2)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{5}}{2*8}=\frac{16-8\sqrt{5}}{16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{5}}{2*8}=\frac{16+8\sqrt{5}}{16}
$