x^2=x+110-x^2

Solution for x^2=x+110-x^2 equation:

x^2=x+110-x^2

We move all terms to the left:

x^2-(x+110-x^2)=0

We get rid of parentheses

x^2+x^2-x-110=0

We add all the numbers together, and all the variables

2x^2-1x-110=0

a = 2; b = -1; c = -110;
Δ = b2-4ac
Δ = -12-4·2·(-110)
Δ = 881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{881}}{2*2}=\frac{1-\sqrt{881}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{881}}{2*2}=\frac{1+\sqrt{881}}{4}
$