9x(x-6)=(2x+2)(x-6)

Solution for 9x(x-6)=(2x+2)(x-6) equation:

9x(x-6)=(2x+2)(x-6)

We move all terms to the left:

9x(x-6)-((2x+2)(x-6))=0

We multiply parentheses

9x^2-54x-((2x+2)(x-6))=0

We multiply parentheses ..

9x^2-((+2x^2-12x+2x-12))-54x=0


We calculate terms in parentheses: -((+2x^2-12x+2x-12)), so:

(+2x^2-12x+2x-12)

We get rid of parentheses

2x^2-12x+2x-12

We add all the numbers together, and all the variables

2x^2-10x-12

Back to the equation:

-(2x^2-10x-12)


We add all the numbers together, and all the variables

9x^2-54x-(2x^2-10x-12)=0

We get rid of parentheses

9x^2-2x^2-54x+10x+12=0

We add all the numbers together, and all the variables

7x^2-44x+12=0

a = 7; b = -44; c = +12;
Δ = b2-4ac
Δ = -442-4·7·12
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-40}{2*7}=\frac{4}{14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+40}{2*7}=\frac{84}{14}
=6
$