(32/x)2=(x+6)(x+2)

Solution for (32/x)2=(x+6)(x+2) equation:

(32/x)2=(x+6)(x+2)

We move all terms to the left:

(32/x)2-((x+6)(x+2))=0


Domain of the equation: x)2!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+32/x)2-((x+6)(x+2))=0

We multiply parentheses

64x-((x+6)(x+2))=0

We multiply parentheses ..

-((+x^2+2x+6x+12))+64x=0


We calculate terms in parentheses: -((+x^2+2x+6x+12)), so:

(+x^2+2x+6x+12)

We get rid of parentheses

x^2+2x+6x+12

We add all the numbers together, and all the variables

x^2+8x+12

Back to the equation:

-(x^2+8x+12)


We add all the numbers together, and all the variables

64x-(x^2+8x+12)=0

We get rid of parentheses

-x^2+64x-8x-12=0

We add all the numbers together, and all the variables

-1x^2+56x-12=0

a = -1; b = 56; c = -12;
Δ = b2-4ac
Δ = 562-4·(-1)·(-12)
Δ = 3088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{193}}{2*-1}=\frac{-56-4\sqrt{193}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{193}}{2*-1}=\frac{-56+4\sqrt{193}}{-2}
$