2/x=8/3x+5

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

2/x=8/3x+5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/3x^2+(-8x)/3x^2-5=0

We multiply all the terms by the denominator


6x+(-8x)-5*3x^2=0

Wy multiply elements

-15x^2+6x+(-8x)=0

We get rid of parentheses

-15x^2+6x-8x=0

We add all the numbers together, and all the variables

-15x^2-2x=0

a = -15; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-15)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-15}=\frac{4}{-30}
=-2/15
$