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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We get rid of parentheses

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

We calculate fractions


5x/15x^2+(-3x)/15x^2-1-1=0

We add all the numbers together, and all the variables

5x/15x^2+(-3x)/15x^2-2=0

We multiply all the terms by the denominator


5x+(-3x)-2*15x^2=0

Wy multiply elements

-30x^2+5x+(-3x)=0

We get rid of parentheses

-30x^2+5x-3x=0

We add all the numbers together, and all the variables

-30x^2+2x=0

a = -30; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-30)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-30}=\frac{-4}{-60}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-30}=\frac{0}{-60}
=0
$