X+8/3x-5=x-8/x+8

Solution for X+8/3x-5=x-8/x+8 equation:

X+8/3X-5=X-8/X+8

We move all terms to the left:

X+8/3X-5-(X-8/X+8)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



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

X∈R


We get rid of parentheses

X+8/3X-X+8/X-8-5=0

We calculate fractions


X-X+8X/3X^2+24X/3X^2-8-5=0

We add all the numbers together, and all the variables

8X/3X^2+24X/3X^2-13=0

We multiply all the terms by the denominator


8X+24X-13*3X^2=0

We add all the numbers together, and all the variables

32X-13*3X^2=0

Wy multiply elements

-39X^2+32X=0

a = -39; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-39)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-39}=\frac{-64}{-78}
=32/39
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-39}=\frac{0}{-78}
=0
$