2/3x-8/5=2/15x

Solution for 2/3x-8/5=2/15x equation:

2/3x-8/5=2/15x

We move all terms to the left:

2/3x-8/5-(2/15x)=0


Domain of the equation: 3x!=0

x!=0/3

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

2/3x-(+2/15x)-8/5=0

We get rid of parentheses

2/3x-2/15x-8/5=0

We calculate fractions


(-360x^2)/1125x^2+750x/1125x^2+(-150x)/1125x^2=0

We multiply all the terms by the denominator


(-360x^2)+750x+(-150x)=0

We get rid of parentheses

-360x^2+750x-150x=0

We add all the numbers together, and all the variables

-360x^2+600x=0

a = -360; b = 600; c = 0;
Δ = b2-4ac
Δ = 6002-4·(-360)·0
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-600}{2*-360}=\frac{-1200}{-720}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+600}{2*-360}=\frac{0}{-720}
=0
$