X+8/x+8=32

Solution for X+8/x+8=32 equation:

X+8/X+8=32

We move all terms to the left:

X+8/X+8-(32)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+8/X-24=0

We multiply all the terms by the denominator


X*X-24*X+8=0

We add all the numbers together, and all the variables

-24X+X*X+8=0

Wy multiply elements

X^2-24X+8=0

a = 1; b = -24; c = +8;
Δ = b2-4ac
Δ = -242-4·1·8
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{34}}{2*1}=\frac{24-4\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{34}}{2*1}=\frac{24+4\sqrt{34}}{2}
$