4/9x=12.9x=

Solution for 4/9x=12.9x= equation:

4/9x=12.9x=

We move all terms to the left:

4/9x-(12.9x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

4/9x-(+12.9x)=0

We get rid of parentheses

4/9x-12.9x=0

We multiply all the terms by the denominator


-(12.9x)*9x+4=0

We add all the numbers together, and all the variables

-(+12.9x)*9x+4=0

We multiply parentheses

-108x^2+4=0

a = -108; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-108)·4
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*-108}=\frac{0-24\sqrt{3}}{-216}
=-\frac{24\sqrt{3}}{-216}
=-\frac{\sqrt{3}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*-108}=\frac{0+24\sqrt{3}}{-216}
=\frac{24\sqrt{3}}{-216}
=\frac{\sqrt{3}}{-9}
$