9x(x-4)=(2x+2)(x-4)

Solution for 9x(x-4)=(2x+2)(x-4) equation:

9x(x-4)=(2x+2)(x-4)

We move all terms to the left:

9x(x-4)-((2x+2)(x-4))=0

We multiply parentheses

9x^2-36x-((2x+2)(x-4))=0

We multiply parentheses ..

9x^2-((+2x^2-8x+2x-8))-36x=0


We calculate terms in parentheses: -((+2x^2-8x+2x-8)), so:

(+2x^2-8x+2x-8)

We get rid of parentheses

2x^2-8x+2x-8

We add all the numbers together, and all the variables

2x^2-6x-8

Back to the equation:

-(2x^2-6x-8)


We add all the numbers together, and all the variables

9x^2-36x-(2x^2-6x-8)=0

We get rid of parentheses

9x^2-2x^2-36x+6x+8=0

We add all the numbers together, and all the variables

7x^2-30x+8=0

a = 7; b = -30; c = +8;
Δ = b2-4ac
Δ = -302-4·7·8
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-26}{2*7}=\frac{4}{14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+26}{2*7}=\frac{56}{14}
=4
$