2/3x=27x=

Solution for 2/3x=27x= equation:

2/3x=27x=

We move all terms to the left:

2/3x-(27x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-27x+2/3x=0

We multiply all the terms by the denominator


-27x*3x+2=0

Wy multiply elements

-81x^2+2=0

a = -81; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-81)·2
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*-81}=\frac{0-18\sqrt{2}}{-162}
=-\frac{18\sqrt{2}}{-162}
=-\frac{\sqrt{2}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*-81}=\frac{0+18\sqrt{2}}{-162}
=\frac{18\sqrt{2}}{-162}
=\frac{\sqrt{2}}{-9}
$