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

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

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

We move all terms to the left:

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

We multiply parentheses

12x^2-6x-(2x+4)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2-8x-4=0

a = 12; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·12·(-4)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*12}=\frac{-8}{24}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*12}=\frac{24}{24}
=1
$