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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(2x+1)+x), so:

3x(2x+1)+x

We add all the numbers together, and all the variables

x+3x(2x+1)

We multiply parentheses

6x^2+x+3x

We add all the numbers together, and all the variables

6x^2+4x

Back to the equation:

-(6x^2+4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2-10x+1=0

a = -6; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-6)·1
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{31}}{2*-6}=\frac{10-2\sqrt{31}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{31}}{2*-6}=\frac{10+2\sqrt{31}}{-12}
$