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

Solution for 2/x+1-1/5=1/3x+3 equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-9x^2)/75x^2+150x/75x^2+(-25x)/75x^2-3+1=0

We add all the numbers together, and all the variables

(-9x^2)/75x^2+150x/75x^2+(-25x)/75x^2-2=0

We multiply all the terms by the denominator


(-9x^2)+150x+(-25x)-2*75x^2=0

Wy multiply elements

(-9x^2)-150x^2+150x+(-25x)=0

We get rid of parentheses

-9x^2-150x^2+150x-25x=0

We add all the numbers together, and all the variables

-159x^2+125x=0

a = -159; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·(-159)·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*-159}=\frac{-250}{-318}
=125/159
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*-159}=\frac{0}{-318}
=0
$