4x(3x+2)+2x(3x-2)=2

Solution for 4x(3x+2)+2x(3x-2)=2 equation:

4x(3x+2)+2x(3x-2)=2

We move all terms to the left:

4x(3x+2)+2x(3x-2)-(2)=0

We multiply parentheses

12x^2+6x^2+8x-4x-2=0

We add all the numbers together, and all the variables

18x^2+4x-2=0

a = 18; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·18·(-2)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*18}=\frac{-4-4\sqrt{10}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*18}=\frac{-4+4\sqrt{10}}{36}
$