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

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

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

We move all terms to the left:

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


Domain of the equation: 15x!=0

x!=0/15

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

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

We get rid of parentheses

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

We calculate fractions


750x^2/675x^2+180x/675x^2+(-270x)/675x^2=0

We multiply all the terms by the denominator


750x^2+180x+(-270x)=0

We get rid of parentheses

750x^2+180x-270x=0

We add all the numbers together, and all the variables

750x^2-90x=0

a = 750; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·750·0
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*750}=\frac{0}{1500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*750}=\frac{180}{1500}
=3/25
$