11x(x+1)=x+1

Solution for 11x(x+1)=x+1 equation:

11x(x+1)=x+1

We move all terms to the left:

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

We multiply parentheses

11x^2+11x-(x+1)=0

We get rid of parentheses

11x^2+11x-x-1=0

We add all the numbers together, and all the variables

11x^2+10x-1=0

a = 11; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·11·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-12}{2*11}=\frac{-22}{22}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+12}{2*11}=\frac{2}{22}
=1/11
$