36-9x=x^2

Solution for 36-9x=x^2 equation:

36-9x=x^2

We move all terms to the left:

36-9x-(x^2)=0

determiningTheFunctionDomain
-x^2-9x+36=0

We add all the numbers together, and all the variables

-1x^2-9x+36=0

a = -1; b = -9; c = +36;
Δ = b2-4ac
Δ = -92-4·(-1)·36
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-1}=\frac{24}{-2}
=-12
$