1/3x+2=3/5x

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

1/3x+2=3/5x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


5x/15x^2+(-9x)/15x^2+2=0

We multiply all the terms by the denominator


5x+(-9x)+2*15x^2=0

Wy multiply elements

30x^2+5x+(-9x)=0

We get rid of parentheses

30x^2+5x-9x=0

We add all the numbers together, and all the variables

30x^2-4x=0

a = 30; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·30·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*30}=\frac{8}{60}
=2/15
$