1/3x+5=2/7x

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

1/3x+5=2/7x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


7x/21x^2+(-6x)/21x^2+5=0

We multiply all the terms by the denominator


7x+(-6x)+5*21x^2=0

Wy multiply elements

105x^2+7x+(-6x)=0

We get rid of parentheses

105x^2+7x-6x=0

We add all the numbers together, and all the variables

105x^2+x=0

a = 105; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·105·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*105}=\frac{-2}{210}
=-1/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*105}=\frac{0}{210}
=0
$