Y=2x2+12x+16

Solution for Y=2x2+12x+16 equation:

=2Y^2+12Y+16

We move all terms to the left:

-(2Y^2+12Y+16)=0

We get rid of parentheses

-2Y^2-12Y-16=0

a = -2; b = -12; c = -16;
Δ = b2-4ac
Δ = -122-4·(-2)·(-16)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*-2}=\frac{8}{-4}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*-2}=\frac{16}{-4}
=-4
$