Y=2x^2+24x+64

Solution for Y=2x^2+24x+64 equation:

=2Y^2+24Y+64

We move all terms to the left:

-(2Y^2+24Y+64)=0

We get rid of parentheses

-2Y^2-24Y-64=0

a = -2; b = -24; c = -64;
Δ = b2-4ac
Δ = -242-4·(-2)·(-64)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8}{2*-2}=\frac{16}{-4}
=-4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8}{2*-2}=\frac{32}{-4}
=-8
$