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

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

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

We move all terms to the left:

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


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


135x^2/1125x^2+300x/1125x^2+(-750x)/1125x^2=0

We multiply all the terms by the denominator


135x^2+300x+(-750x)=0

We get rid of parentheses

135x^2+300x-750x=0

We add all the numbers together, and all the variables

135x^2-450x=0

a = 135; b = -450; c = 0;
Δ = b2-4ac
Δ = -4502-4·135·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-450}{2*135}=\frac{0}{270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+450}{2*135}=\frac{900}{270}
=3+1/3
$