Y=2x^2-24x+8

Solution for Y=2x^2-24x+8 equation:

=2Y^2-24Y+8

We move all terms to the left:

-(2Y^2-24Y+8)=0

We get rid of parentheses

-2Y^2+24Y-8=0

a = -2; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·(-2)·(-8)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{2}}{2*-2}=\frac{-24-16\sqrt{2}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{2}}{2*-2}=\frac{-24+16\sqrt{2}}{-4}
$