x(11x+2)=11

Solution for x(11x+2)=11 equation:

x(11x+2)=11

We move all terms to the left:

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

We multiply parentheses

11x^2+2x-11=0

a = 11; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·11·(-11)
Δ = 488
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:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{122}}{2*11}=\frac{-2-2\sqrt{122}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{122}}{2*11}=\frac{-2+2\sqrt{122}}{22}
$