x/6=x/14x

Solution for x/6=x/14x equation:

x/6=x/14x

We move all terms to the left:

x/6-(x/14x)=0


Domain of the equation: 14x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x/6-(+x/14x)=0

We get rid of parentheses

x/6-x/14x=0

We calculate fractions


14x^2/84x+(-6x)/84x=0

We multiply all the terms by the denominator


14x^2+(-6x)=0

We get rid of parentheses

14x^2-6x=0

a = 14; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·14·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*14}=\frac{12}{28}
=3/7
$