1/7x=21x=

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Solution for 1/7x=21x= equation:



1/7x=21x=
We move all terms to the left:
1/7x-(21x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
We add all the numbers together, and all the variables
-21x+1/7x=0
We multiply all the terms by the denominator
-21x*7x+1=0
Wy multiply elements
-147x^2+1=0
a = -147; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-147)·1
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*-147}=\frac{0-14\sqrt{3}}{-294} =-\frac{14\sqrt{3}}{-294} =-\frac{\sqrt{3}}{-21} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-147}=\frac{0+14\sqrt{3}}{-294} =\frac{14\sqrt{3}}{-294} =\frac{\sqrt{3}}{-21} $

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