2/3x-5=1/x+8

Solution for 2/3x-5=1/x+8 equation:

2/3x-5=1/x+8

We move all terms to the left:

2/3x-5-(1/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

2/3x-1/x-8-5=0

We calculate fractions


2x/3x^2+(-3x)/3x^2-8-5=0

We add all the numbers together, and all the variables

2x/3x^2+(-3x)/3x^2-13=0

We multiply all the terms by the denominator


2x+(-3x)-13*3x^2=0

Wy multiply elements

-39x^2+2x+(-3x)=0

We get rid of parentheses

-39x^2+2x-3x=0

We add all the numbers together, and all the variables

-39x^2-1x=0

a = -39; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-39)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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