2/5x-5/3x=1/15

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

2/5x-5/3x=1/15

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-45x^2)/225x^2+90x/225x^2+(-375x)/225x^2=0

We multiply all the terms by the denominator


(-45x^2)+90x+(-375x)=0

We get rid of parentheses

-45x^2+90x-375x=0

We add all the numbers together, and all the variables

-45x^2-285x=0

a = -45; b = -285; c = 0;
Δ = b2-4ac
Δ = -2852-4·(-45)·0
Δ = 81225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81225}=285$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-285)-285}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-285)+285}{2*-45}=\frac{570}{-90}
=-6+1/3
$