(6x+1)x=(3x-2)(6x+1)

Solution for (6x+1)x=(3x-2)(6x+1) equation:

(6x+1)x=(3x-2)(6x+1)

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

6x^2-((+18x^2+3x-12x-2))+x=0


We calculate terms in parentheses: -((+18x^2+3x-12x-2)), so:

(+18x^2+3x-12x-2)

We get rid of parentheses

18x^2+3x-12x-2

We add all the numbers together, and all the variables

18x^2-9x-2

Back to the equation:

-(18x^2-9x-2)


We add all the numbers together, and all the variables

6x^2+x-(18x^2-9x-2)=0

We get rid of parentheses

6x^2-18x^2+x+9x+2=0

We add all the numbers together, and all the variables

-12x^2+10x+2=0

a = -12; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·(-12)·2
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-12}=\frac{-24}{-24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-12}=\frac{4}{-24}
=-1/6
$