7/21x=x

Solution for 7/21x=x equation:

7/21x=x

We move all terms to the left:

7/21x-(x)=0


Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/21x=0

We multiply all the terms by the denominator


-1x*21x+7=0

Wy multiply elements

-21x^2+7=0

a = -21; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-21)·7
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*-21}=\frac{0-14\sqrt{3}}{-42}
=-\frac{14\sqrt{3}}{-42}
=-\frac{\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-21}=\frac{0+14\sqrt{3}}{-42}
=\frac{14\sqrt{3}}{-42}
=\frac{\sqrt{3}}{-3}
$