111=x2+11

Solution for 111=x2+11 equation:

111=x2+11

We move all terms to the left:

111-(x2+11)=0

We add all the numbers together, and all the variables

-(+x^2+11)+111=0

We get rid of parentheses

-x^2-11+111=0

We add all the numbers together, and all the variables

-1x^2+100=0

a = -1; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-1)·100
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-1}=\frac{20}{-2}
=-10
$