5/x+1/3x=1x/3

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

5/x+1/3x=1x/3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-1x^2)/27x^2+135x/27x^2+x/27x^2=0

We multiply all the terms by the denominator


(-1x^2)+135x+x=0

We add all the numbers together, and all the variables

(-1x^2)+136x=0

We get rid of parentheses

-1x^2+136x=0

a = -1; b = 136; c = 0;
Δ = b2-4ac
Δ = 1362-4·(-1)·0
Δ = 18496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18496}=136$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-136}{2*-1}=\frac{-272}{-2}
=+136
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+136}{2*-1}=\frac{0}{-2}
=0
$