1/7x=4/x+2

Solution for 1/7x=4/x+2 equation:

1/7x=4/x+2

We move all terms to the left:

1/7x-(4/x+2)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/7x-4/x-2=0

We calculate fractions


x/7x^2+(-28x)/7x^2-2=0

We multiply all the terms by the denominator


x+(-28x)-2*7x^2=0

Wy multiply elements

-14x^2+x+(-28x)=0

We get rid of parentheses

-14x^2+x-28x=0

We add all the numbers together, and all the variables

-14x^2-27x=0

a = -14; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-14)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-14}=\frac{54}{-28}
=-1+13/14
$