Y=2x2+12x-32

Solution for Y=2x2+12x-32 equation:

=2Y^2+12Y-32

We move all terms to the left:

-(2Y^2+12Y-32)=0

We get rid of parentheses

-2Y^2-12Y+32=0

a = -2; b = -12; c = +32;
Δ = b2-4ac
Δ = -122-4·(-2)·32
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*-2}=\frac{-8}{-4}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*-2}=\frac{32}{-4}
=-8
$