((x-6)*(x-6))/(x+12)=9

Solution for ((x-6)*(x-6))/(x+12)=9 equation:

((x-6)(x-6))/(x+12)=9

We move all terms to the left:

((x-6)(x-6))/(x+12)-(9)=0


Domain of the equation: (x+12)!=0

We move all terms containing x to the left, all other terms to the right

x!=-12

x∈R


We multiply parentheses ..

((+x^2-6x-6x+36))/(x+12)-9=0

We multiply all the terms by the denominator


((+x^2-6x-6x+36))-9*(x+12)=0


We calculate terms in parentheses: +((+x^2-6x-6x+36)), so:

(+x^2-6x-6x+36)

We get rid of parentheses

x^2-6x-6x+36

We add all the numbers together, and all the variables

x^2-12x+36

Back to the equation:

+(x^2-12x+36)


We multiply parentheses

(x^2-12x+36)-9x-108=0

We get rid of parentheses

x^2-12x-9x+36-108=0

We add all the numbers together, and all the variables

x^2-21x-72=0

a = 1; b = -21; c = -72;
Δ = b2-4ac
Δ = -212-4·1·(-72)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-27}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*1}=\frac{48}{2}
=24
$