22+x=x^2

Solution for 22+x=x^2 equation:

22+x=x^2

We move all terms to the left:

22+x-(x^2)=0

determiningTheFunctionDomain
-x^2+x+22=0

We add all the numbers together, and all the variables

-1x^2+x+22=0

a = -1; b = 1; c = +22;
Δ = b2-4ac
Δ = 12-4·(-1)·22
Δ = 89
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{89}}{2*-1}=\frac{-1-\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{89}}{2*-1}=\frac{-1+\sqrt{89}}{-2}
$