9x=x^2+9

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

9x=x^2+9

We move all terms to the left:

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

We get rid of parentheses

-x^2+9x-9=0

We add all the numbers together, and all the variables

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

a = -1; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·(-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{-(9)-3\sqrt{5}}{2*-1}=\frac{-9-3\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*-1}=\frac{-9+3\sqrt{5}}{-2}
$