1/7x=2/3x+2

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

1/7x=2/3x+2

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/21x^2+(-14x)/21x^2-2=0

We multiply all the terms by the denominator


3x+(-14x)-2*21x^2=0

Wy multiply elements

-42x^2+3x+(-14x)=0

We get rid of parentheses

-42x^2+3x-14x=0

We add all the numbers together, and all the variables

-42x^2-11x=0

a = -42; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-42)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-42}=\frac{0}{-84}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-42}=\frac{22}{-84}
=-11/42
$