3/7x-1/3x=2

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

3/7x-1/3x=2

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


9x/21x^2+(-7x)/21x^2-2=0

We multiply all the terms by the denominator


9x+(-7x)-2*21x^2=0

Wy multiply elements

-42x^2+9x+(-7x)=0

We get rid of parentheses

-42x^2+9x-7x=0

We add all the numbers together, and all the variables

-42x^2+2x=0

a = -42; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-42)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-42}=\frac{-4}{-84}
=1/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-42}=\frac{0}{-84}
=0
$