2x-9=x^2-12x+36

Solution for 2x-9=x^2-12x+36 equation:

2x-9=x^2-12x+36

We move all terms to the left:

2x-9-(x^2-12x+36)=0

We get rid of parentheses

-x^2+2x+12x-36-9=0

We add all the numbers together, and all the variables

-1x^2+14x-45=0

a = -1; b = 14; c = -45;
Δ = b2-4ac
Δ = 142-4·(-1)·(-45)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*-1}=\frac{-10}{-2}
=+5
$