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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

9x/18x^2+(-2x)/18x^2+6=0

We multiply all the terms by the denominator


9x+(-2x)+6*18x^2=0

Wy multiply elements

108x^2+9x+(-2x)=0

We get rid of parentheses

108x^2+9x-2x=0

We add all the numbers together, and all the variables

108x^2+7x=0

a = 108; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·108·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*108}=\frac{-14}{216}
=-7/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*108}=\frac{0}{216}
=0
$