4/9x*2-4/3x=-1

Solution for 4/9x*2-4/3x=-1 equation:

4/9x*2-4/3x=-1

We move all terms to the left:

4/9x*2-4/3x-(-1)=0


Domain of the equation: 9x*2!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/9x*2-4/3x+1=0

We calculate fractions


12x/162x^2+(-144x)/162x^2+1=0

We multiply all the terms by the denominator


12x+(-144x)+1*162x^2=0

Wy multiply elements

162x^2+12x+(-144x)=0

We get rid of parentheses

162x^2+12x-144x=0

We add all the numbers together, and all the variables

162x^2-132x=0

a = 162; b = -132; c = 0;
Δ = b2-4ac
Δ = -1322-4·162·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-132}{2*162}=\frac{0}{324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+132}{2*162}=\frac{264}{324}
=22/27
$