1/3x=22x

Solution for 1/3x=22x equation:

1/3x=22x

We move all terms to the left:

1/3x-(22x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-22x+1/3x=0

We multiply all the terms by the denominator


-22x*3x+1=0

Wy multiply elements

-66x^2+1=0

a = -66; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-66)·1
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*-66}=\frac{0-2\sqrt{66}}{-132}
=-\frac{2\sqrt{66}}{-132}
=-\frac{\sqrt{66}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*-66}=\frac{0+2\sqrt{66}}{-132}
=\frac{2\sqrt{66}}{-132}
=\frac{\sqrt{66}}{-66}
$