2/9x-3=3/11x

Solution for 2/9x-3=3/11x equation:

2/9x-3=3/11x

We move all terms to the left:

2/9x-3-(3/11x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 11x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/9x-(+3/11x)-3=0

We get rid of parentheses

2/9x-3/11x-3=0

We calculate fractions


22x/99x^2+(-27x)/99x^2-3=0

We multiply all the terms by the denominator


22x+(-27x)-3*99x^2=0

Wy multiply elements

-297x^2+22x+(-27x)=0

We get rid of parentheses

-297x^2+22x-27x=0

We add all the numbers together, and all the variables

-297x^2-5x=0

a = -297; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-297)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-297}=\frac{0}{-594}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-297}=\frac{10}{-594}
=-5/297
$