2(x^2+8x+12)=0

Solution for 2(x^2+8x+12)=0 equation:

2(x^2+8x+12)=0

We multiply parentheses

2x^2+16x+24=0

a = 2; b = 16; c = +24;
Δ = b2-4ac
Δ = 162-4·2·24
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*2}=\frac{-8}{4}
=-2
$