x+8-(8/x+8)=16

Solution for x+8-(8/x+8)=16 equation:

x+8-(8/x+8)=16

We move all terms to the left:

x+8-(8/x+8)-(16)=0


Domain of the equation: x+8)!=0

x∈R


We add all the numbers together, and all the variables

x-(8/x+8)-8=0

We get rid of parentheses

x-8/x-8-8=0

We multiply all the terms by the denominator


x*x-8*x-8*x-8=0

We add all the numbers together, and all the variables

-16x+x*x-8=0

Wy multiply elements

x^2-16x-8=0

a = 1; b = -16; c = -8;
Δ = b2-4ac
Δ = -162-4·1·(-8)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*1}=\frac{16-12\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*1}=\frac{16+12\sqrt{2}}{2}
$