2/5x-3/7x=1/15

Solution for 2/5x-3/7x=1/15 equation:

2/5x-3/7x=1/15

We move all terms to the left:

2/5x-3/7x-(1/15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-3/7x-(+1/15)=0

We get rid of parentheses

2/5x-3/7x-1/15=0

We calculate fractions


(-245x^2)/525x^2+210x/525x^2+(-225x)/525x^2=0

We multiply all the terms by the denominator


(-245x^2)+210x+(-225x)=0

We get rid of parentheses

-245x^2+210x-225x=0

We add all the numbers together, and all the variables

-245x^2-15x=0

a = -245; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-245)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-245}=\frac{0}{-490}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-245}=\frac{30}{-490}
=-3/49
$