9+3x=x^2

Solution for 9+3x=x^2 equation:

9+3x=x^2

We move all terms to the left:

9+3x-(x^2)=0

determiningTheFunctionDomain
-x^2+3x+9=0

We add all the numbers together, and all the variables

-1x^2+3x+9=0

a = -1; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-1)·9
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{-(3)-3\sqrt{5}}{2*-1}=\frac{-3-3\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{5}}{2*-1}=\frac{-3+3\sqrt{5}}{-2}
$