9/3x+5=6+5/9x

Solution for 9/3x+5=6+5/9x equation:

9/3x+5=6+5/9x

We move all terms to the left:

9/3x+5-(6+5/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/3x-(5/9x+6)+5=0

We get rid of parentheses

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

We calculate fractions


81x/27x^2+(-15x)/27x^2-6+5=0

We add all the numbers together, and all the variables

81x/27x^2+(-15x)/27x^2-1=0

We multiply all the terms by the denominator


81x+(-15x)-1*27x^2=0

Wy multiply elements

-27x^2+81x+(-15x)=0

We get rid of parentheses

-27x^2+81x-15x=0

We add all the numbers together, and all the variables

-27x^2+66x=0

a = -27; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-27)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-27}=\frac{-132}{-54}
=2+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-27}=\frac{0}{-54}
=0
$