1/7x=21x=

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}
$