2(x^2+7x+12)=0

Solution for 2(x^2+7x+12)=0 equation:

2(x^2+7x+12)=0

We multiply parentheses

2x^2+14x+24=0

a = 2; b = 14; c = +24;
Δ = b2-4ac
Δ = 142-4·2·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*2}=\frac{-12}{4}
=-3
$