180-9x=x^2

Solution for 180-9x=x^2 equation:

180-9x=x^2

We move all terms to the left:

180-9x-(x^2)=0

determiningTheFunctionDomain
-x^2-9x+180=0

We add all the numbers together, and all the variables

-1x^2-9x+180=0

a = -1; b = -9; c = +180;
Δ = b2-4ac
Δ = -92-4·(-1)·180
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{89}}{2*-1}=\frac{9-3\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{89}}{2*-1}=\frac{9+3\sqrt{89}}{-2}
$