x+6=x^2-12x+36

Solution for x+6=x^2-12x+36 equation:

x+6=x^2-12x+36

We move all terms to the left:

x+6-(x^2-12x+36)=0

We get rid of parentheses

-x^2+x+12x-36+6=0

We add all the numbers together, and all the variables

-1x^2+13x-30=0

a = -1; b = 13; c = -30;
Δ = b2-4ac
Δ = 132-4·(-1)·(-30)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-1}=\frac{-6}{-2}
=+3
$