7x=1/3x

Solution for 7x=1/3x equation:

7x=1/3x

We move all terms to the left:

7x-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7x-1/3x=0

We multiply all the terms by the denominator


7x*3x-1=0

Wy multiply elements

21x^2-1=0

a = 21; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·21·(-1)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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