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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We get rid of parentheses

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

We calculate fractions


(-1029x^2)/315x^2+105x/315x^2+(-45x)/315x^2=0

We multiply all the terms by the denominator


(-1029x^2)+105x+(-45x)=0

We get rid of parentheses

-1029x^2+105x-45x=0

We add all the numbers together, and all the variables

-1029x^2+60x=0

a = -1029; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-1029)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-1029}=\frac{-120}{-2058}
=20/343
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-1029}=\frac{0}{-2058}
=0
$