1/3x-1/5x=7/30

Solution for 1/3x-1/5x=7/30 equation:

1/3x-1/5x=7/30

We move all terms to the left:

1/3x-1/5x-(7/30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/5x-(+7/30)=0

We get rid of parentheses

1/3x-1/5x-7/30=0

We calculate fractions


(-525x^2)/1350x^2+450x/1350x^2+(-270x)/1350x^2=0

We multiply all the terms by the denominator


(-525x^2)+450x+(-270x)=0

We get rid of parentheses

-525x^2+450x-270x=0

We add all the numbers together, and all the variables

-525x^2+180x=0

a = -525; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-525)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-525}=\frac{-360}{-1050}
=12/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-525}=\frac{0}{-1050}
=0
$