(8/9)x=1/3

Solution for (8/9)x=1/3 equation:

(8/9)x=1/3

We move all terms to the left:

(8/9)x-(1/3)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/9)x-(+1/3)=0

We multiply parentheses

8x^2-(+1/3)=0

We get rid of parentheses

8x^2-1/3=0

We multiply all the terms by the denominator


8x^2*3-1=0

Wy multiply elements

24x^2-1=0

a = 24; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·24·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*24}=\frac{0-4\sqrt{6}}{48}
=-\frac{4\sqrt{6}}{48}
=-\frac{\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*24}=\frac{0+4\sqrt{6}}{48}
=\frac{4\sqrt{6}}{48}
=\frac{\sqrt{6}}{12}
$