2x^2+12x=-4

Solution for 2x^2+12x=-4 equation:

2x^2+12x=-4

We move all terms to the left:

2x^2+12x-(-4)=0

We add all the numbers together, and all the variables

2x^2+12x+4=0

a = 2; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·2·4
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*2}=\frac{-12-4\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*2}=\frac{-12+4\sqrt{7}}{4}
$