1/3x=9x

Solution for 1/3x=9x equation:

1/3x=9x

We move all terms to the left:

1/3x-(9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+1/3x=0

We multiply all the terms by the denominator


-9x*3x+1=0

Wy multiply elements

-27x^2+1=0

a = -27; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-27)·1
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-27}=\frac{0-6\sqrt{3}}{-54}
=-\frac{6\sqrt{3}}{-54}
=-\frac{\sqrt{3}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-27}=\frac{0+6\sqrt{3}}{-54}
=\frac{6\sqrt{3}}{-54}
=\frac{\sqrt{3}}{-9}
$