3(2/3)x=2/9

Solution for 3(2/3)x=2/9 equation:

3(2/3)x=2/9

We move all terms to the left:

3(2/3)x-(2/9)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(+2/3)x-(+2/9)=0

We multiply parentheses

6x^2-(+2/9)=0

We get rid of parentheses

6x^2-2/9=0

We multiply all the terms by the denominator


6x^2*9-2=0

Wy multiply elements

54x^2-2=0

a = 54; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·54·(-2)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*54}=\frac{0-12\sqrt{3}}{108}
=-\frac{12\sqrt{3}}{108}
=-\frac{\sqrt{3}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*54}=\frac{0+12\sqrt{3}}{108}
=\frac{12\sqrt{3}}{108}
=\frac{\sqrt{3}}{9}
$