11=x^2+2x-11

Solution for 11=x^2+2x-11 equation:

11=x^2+2x-11

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-2x+22=0

a = -1; b = -2; c = +22;
Δ = b2-4ac
Δ = -22-4·(-1)·22
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{23}}{2*-1}=\frac{2-2\sqrt{23}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{23}}{2*-1}=\frac{2+2\sqrt{23}}{-2}
$