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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

30x^2+3x-5x=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{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*30}=\frac{4}{60}
=1/15
$