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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

42x^2+7x-9x=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{0}{84}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*42}=\frac{4}{84}
=1/21
$