0=2x^2+12x+4

Solution for 0=2x^2+12x+4 equation:

0=2x^2+12x+4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-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}
$