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

Solution for 3x(x-1)+2x(4x-1)=x equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2+8x^2-1x-3x-2x=0

We add all the numbers together, and all the variables

11x^2-6x=0

a = 11; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·11·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*11}=\frac{0}{22}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*11}=\frac{12}{22}
=6/11
$