(1/3)x=6/9

Solution for (1/3)x=6/9 equation:

(1/3)x=6/9

We move all terms to the left:

(1/3)x-(6/9)=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

(+1/3)x-(+6/9)=0

We multiply parentheses

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

We get rid of parentheses

x^2-6/9=0

We multiply all the terms by the denominator


x^2*9-6=0

Wy multiply elements

9x^2-6=0

a = 9; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·9·(-6)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*9}=\frac{0-6\sqrt{6}}{18}
=-\frac{6\sqrt{6}}{18}
=-\frac{\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*9}=\frac{0+6\sqrt{6}}{18}
=\frac{6\sqrt{6}}{18}
=\frac{\sqrt{6}}{3}
$