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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


125x/375x^2+(-3x)/375x^2+(-3x)/375x^2-1=0

We multiply all the terms by the denominator


125x+(-3x)+(-3x)-1*375x^2=0

Wy multiply elements

-375x^2+125x+(-3x)+(-3x)=0

We get rid of parentheses

-375x^2+125x-3x-3x=0

We add all the numbers together, and all the variables

-375x^2+119x=0

a = -375; b = 119; c = 0;
Δ = b2-4ac
Δ = 1192-4·(-375)·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(119)-119}{2*-375}=\frac{-238}{-750}
=119/375
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(119)+119}{2*-375}=\frac{0}{-750}
=0
$