2a^2+12a+8=2

Solution for 2a^2+12a+8=2 equation:

2a^2+12a+8=2

We move all terms to the left:

2a^2+12a+8-(2)=0

We add all the numbers together, and all the variables

2a^2+12a+6=0

a = 2; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·2·6
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*2}=\frac{-12-4\sqrt{6}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*2}=\frac{-12+4\sqrt{6}}{4}
$