(6x+4)(x-2)=6

Solution for (6x+4)(x-2)=6 equation:

(6x+4)(x-2)=6

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-8x-14=0

a = 6; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·6·(-14)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*6}=\frac{28}{12}
=2+1/3
$