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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+6x^2-3x+4x-2)-1x=0

We get rid of parentheses

6x^2-3x+4x-1x-2=0

We add all the numbers together, and all the variables

6x^2-2=0

a = 6; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·6·(-2)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*6}=\frac{0-4\sqrt{3}}{12}
=-\frac{4\sqrt{3}}{12}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*6}=\frac{0+4\sqrt{3}}{12}
=\frac{4\sqrt{3}}{12}
=\frac{\sqrt{3}}{3}
$