x+11=x2

Solution for x+11=x2 equation:

x+11=x2

We move all terms to the left:

x+11-(x2)=0

We add all the numbers together, and all the variables

-1x^2+x+11=0

a = -1; b = 1; c = +11;
Δ = b2-4ac
Δ = 12-4·(-1)·11
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{5}}{2*-1}=\frac{-1-3\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{5}}{2*-1}=\frac{-1+3\sqrt{5}}{-2}
$