1/3x-7/15x=1/5

Solution for 1/3x-7/15x=1/5 equation:

1/3x-7/15x=1/5

We move all terms to the left:

1/3x-7/15x-(1/5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-7/15x-(+1/5)=0

We get rid of parentheses

1/3x-7/15x-1/5=0

We calculate fractions


(-45x^2)/1125x^2+375x/1125x^2+(-525x)/1125x^2=0

We multiply all the terms by the denominator


(-45x^2)+375x+(-525x)=0

We get rid of parentheses

-45x^2+375x-525x=0

We add all the numbers together, and all the variables

-45x^2-150x=0

a = -45; b = -150; c = 0;
Δ = b2-4ac
Δ = -1502-4·(-45)·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150}{2*-45}=\frac{300}{-90}
=-3+1/3
$