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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/3x^2+(-9x)/3x^2-5-2=0

We add all the numbers together, and all the variables

8x/3x^2+(-9x)/3x^2-7=0

We multiply all the terms by the denominator


8x+(-9x)-7*3x^2=0

Wy multiply elements

-21x^2+8x+(-9x)=0

We get rid of parentheses

-21x^2+8x-9x=0

We add all the numbers together, and all the variables

-21x^2-1x=0

a = -21; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-21)·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*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-21}=\frac{2}{-42}
=-1/21
$