(1/x)+(1/5x)=1/3

Solution for (1/x)+(1/5x)=1/3 equation:

(1/x)+(1/5x)=1/3

We move all terms to the left:

(1/x)+(1/5x)-(1/3)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/x)+(+1/5x)-(+1/3)=0

We get rid of parentheses

1/x+1/5x-1/3=0

We calculate fractions


(-25x^2)/45x^2+45x/45x^2+9x/45x^2=0

We multiply all the terms by the denominator


(-25x^2)+45x+9x=0

We add all the numbers together, and all the variables

(-25x^2)+54x=0

We get rid of parentheses

-25x^2+54x=0

a = -25; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-25)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-25}=\frac{-108}{-50}
=2+4/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-25}=\frac{0}{-50}
=0
$