2/3x-6=7/9x-5

Solution for 2/3x-6=7/9x-5 equation:

2/3x-6=7/9x-5

We move all terms to the left:

2/3x-6-(7/9x-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x-5)!=0

x∈R


We get rid of parentheses

2/3x-7/9x+5-6=0

We calculate fractions


18x/27x^2+(-21x)/27x^2+5-6=0

We add all the numbers together, and all the variables

18x/27x^2+(-21x)/27x^2-1=0

We multiply all the terms by the denominator


18x+(-21x)-1*27x^2=0

Wy multiply elements

-27x^2+18x+(-21x)=0

We get rid of parentheses

-27x^2+18x-21x=0

We add all the numbers together, and all the variables

-27x^2-3x=0

a = -27; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-27)·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*-27}=\frac{0}{-54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-27}=\frac{6}{-54}
=-1/9
$