x+9=x^2

Solution for x+9=x^2 equation:

x+9=x^2

We move all terms to the left:

x+9-(x^2)=0

determiningTheFunctionDomain
-x^2+x+9=0

We add all the numbers together, and all the variables

-1x^2+x+9=0

a = -1; b = 1; c = +9;
Δ = b2-4ac
Δ = 12-4·(-1)·9
Δ = 37
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{37}}{2*-1}=\frac{-1-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*-1}=\frac{-1+\sqrt{37}}{-2}
$