2x(3x+2)=3x+2

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

2x(3x+2)=3x+2

We move all terms to the left:

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

We multiply parentheses

6x^2+4x-(3x+2)=0

We get rid of parentheses

6x^2+4x-3x-2=0

We add all the numbers together, and all the variables

6x^2+x-2=0

a = 6; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·6·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*6}=\frac{6}{12}
=1/2
$