(2/x)+(5/3x)=5

Solution for (2/x)+(5/3x)=5 equation:

(2/x)+(5/3x)=5

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


6x/3x^2+5x/3x^2-5=0

We multiply all the terms by the denominator


6x+5x-5*3x^2=0

We add all the numbers together, and all the variables

11x-5*3x^2=0

Wy multiply elements

-15x^2+11x=0

a = -15; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-15)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-15}=\frac{-22}{-30}
=11/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-15}=\frac{0}{-30}
=0
$