1/9x+1/2x+2/9=8/3

Solution for 1/9x+1/2x+2/9=8/3 equation:

1/9x+1/2x+2/9=8/3

We move all terms to the left:

1/9x+1/2x+2/9-(8/3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/9x+1/2x+2/9-(+8/3)=0

We get rid of parentheses

1/9x+1/2x+2/9-8/3=0

We calculate fractions


(-2592x^2)/4374x^2+18x/4374x^2+2187x/4374x^2+36x/4374x^2=0

We multiply all the terms by the denominator


(-2592x^2)+18x+2187x+36x=0

We add all the numbers together, and all the variables

(-2592x^2)+2241x=0

We get rid of parentheses

-2592x^2+2241x=0

a = -2592; b = 2241; c = 0;
Δ = b2-4ac
Δ = 22412-4·(-2592)·0
Δ = 5022081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5022081}=2241$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2241)-2241}{2*-2592}=\frac{-4482}{-5184}
=83/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2241)+2241}{2*-2592}=\frac{0}{-5184}
=0
$