2/5x+1/3=4/15x

Solution for 2/5x+1/3=4/15x equation:

2/5x+1/3=4/15x

We move all terms to the left:

2/5x+1/3-(4/15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(+4/15x)+1/3=0

We get rid of parentheses

2/5x-4/15x+1/3=0

We calculate fractions


75x^2/675x^2+270x/675x^2+(-180x)/675x^2=0

We multiply all the terms by the denominator


75x^2+270x+(-180x)=0

We get rid of parentheses

75x^2+270x-180x=0

We add all the numbers together, and all the variables

75x^2+90x=0

a = 75; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·75·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*75}=\frac{-180}{150}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*75}=\frac{0}{150}
=0
$