(11x+1)(6x-5)=x

Solution for (11x+1)(6x-5)=x equation:

(11x+1)(6x-5)=x

We move all terms to the left:

(11x+1)(6x-5)-(x)=0

We add all the numbers together, and all the variables

-1x+(11x+1)(6x-5)=0

We multiply parentheses ..

(+66x^2-55x+6x-5)-1x=0

We get rid of parentheses

66x^2-55x+6x-1x-5=0

We add all the numbers together, and all the variables

66x^2-50x-5=0

a = 66; b = -50; c = -5;
Δ = b2-4ac
Δ = -502-4·66·(-5)
Δ = 3820
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:

$\sqrt{\Delta}=\sqrt{3820}=\sqrt{4*955}=\sqrt{4}*\sqrt{955}=2\sqrt{955}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{955}}{2*66}=\frac{50-2\sqrt{955}}{132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{955}}{2*66}=\frac{50+2\sqrt{955}}{132}
$