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

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

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

We move all terms to the left:

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

We calculate fractions


125x/375x^2+(-3x)/375x^2+(-9x)/375x^2+1=0

We multiply all the terms by the denominator


125x+(-3x)+(-9x)+1*375x^2=0

Wy multiply elements

375x^2+125x+(-3x)+(-9x)=0

We get rid of parentheses

375x^2+125x-3x-9x=0

We add all the numbers together, and all the variables

375x^2+113x=0

a = 375; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·375·0
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*375}=\frac{-226}{750}
=-113/375
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*375}=\frac{0}{750}
=0
$