(2/3x)+(4/9x)=1

Solution for (2/3x)+(4/9x)=1 equation:

(2/3x)+(4/9x)=1

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


18x/27x^2+12x/27x^2-1=0

We multiply all the terms by the denominator


18x+12x-1*27x^2=0

We add all the numbers together, and all the variables

30x-1*27x^2=0

Wy multiply elements

-27x^2+30x=0

a = -27; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-27)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-27}=\frac{-60}{-54}
=1+1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-27}=\frac{0}{-54}
=0
$