(4/9)x=4/54

Solution for (4/9)x=4/54 equation:

(4/9)x=4/54

We move all terms to the left:

(4/9)x-(4/54)=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

(+4/9)x-(+4/54)=0

We multiply parentheses

4x^2-(+4/54)=0

We get rid of parentheses

4x^2-4/54=0

We multiply all the terms by the denominator


4x^2*54-4=0

Wy multiply elements

216x^2-4=0

a = 216; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·216·(-4)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*216}=\frac{0-24\sqrt{6}}{432}
=-\frac{24\sqrt{6}}{432}
=-\frac{\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*216}=\frac{0+24\sqrt{6}}{432}
=\frac{24\sqrt{6}}{432}
=\frac{\sqrt{6}}{18}
$