(3x+1)(2x+2)=x

Solution for (3x+1)(2x+2)=x equation:

(3x+1)(2x+2)=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+6x^2+6x+2x+2)-1x=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+7x+2=0

a = 6; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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