32/6x+6=9/9x+9

Solution for 32/6x+6=9/9x+9 equation:

32/6x+6=9/9x+9

We move all terms to the left:

32/6x+6-(9/9x+9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

32/6x-9/9x-9+6=0

We calculate fractions


288x/54x^2+(-54x)/54x^2-9+6=0

We add all the numbers together, and all the variables

288x/54x^2+(-54x)/54x^2-3=0

We multiply all the terms by the denominator


288x+(-54x)-3*54x^2=0

Wy multiply elements

-162x^2+288x+(-54x)=0

We get rid of parentheses

-162x^2+288x-54x=0

We add all the numbers together, and all the variables

-162x^2+234x=0

a = -162; b = 234; c = 0;
Δ = b2-4ac
Δ = 2342-4·(-162)·0
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-234}{2*-162}=\frac{-468}{-324}
=1+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+234}{2*-162}=\frac{0}{-324}
=0
$