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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+3x^2-18x+x-6)-1x=0

We get rid of parentheses

3x^2-18x+x-1x-6=0

We add all the numbers together, and all the variables

3x^2-18x-6=0

a = 3; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·3·(-6)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{11}}{2*3}=\frac{18-6\sqrt{11}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{11}}{2*3}=\frac{18+6\sqrt{11}}{6}
$