2/3(x)-5/9(x)=3

Solution for 2/3(x)-5/9(x)=3 equation:

2/3(x)-5/9(x)=3

We move all terms to the left:

2/3(x)-5/9(x)-(3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


18x/27x^2+(-15x)/27x^2-3=0

We multiply all the terms by the denominator


18x+(-15x)-3*27x^2=0

Wy multiply elements

-81x^2+18x+(-15x)=0

We get rid of parentheses

-81x^2+18x-15x=0

We add all the numbers together, and all the variables

-81x^2+3x=0

a = -81; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-81)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-81}=\frac{-6}{-162}
=1/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-81}=\frac{0}{-162}
=0
$