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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+3x(2x+4)=0

We multiply parentheses

6x^2-1x+12x=0

We add all the numbers together, and all the variables

6x^2+11x=0

a = 6; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·6·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*6}=\frac{-22}{12}
=-1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*6}=\frac{0}{12}
=0
$