1/9x+2/18=1/3x-2

Solution for 1/9x+2/18=1/3x-2 equation:

1/9x+2/18=1/3x-2

We move all terms to the left:

1/9x+2/18-(1/3x-2)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

1/9x-1/3x+2+2/18=0

We calculate fractions


162x^2/486x^2+54x/486x^2+(-162x)/486x^2+2=0

We multiply all the terms by the denominator


162x^2+54x+(-162x)+2*486x^2=0

Wy multiply elements

162x^2+972x^2+54x+(-162x)=0

We get rid of parentheses

162x^2+972x^2+54x-162x=0

We add all the numbers together, and all the variables

1134x^2-108x=0

a = 1134; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·1134·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*1134}=\frac{0}{2268}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*1134}=\frac{216}{2268}
=2/21
$