4+6k+6k^2+2k=2

Solution for 4+6k+6k^2+2k=2 equation:

4+6k+6k^2+2k=2

We move all terms to the left:

4+6k+6k^2+2k-(2)=0

We add all the numbers together, and all the variables

6k^2+8k+2=0

a = 6; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·6·2
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*6}=\frac{-12}{12}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*6}=\frac{-4}{12}
=-1/3
$