32/6x+6=34/9x-9

Solution for 32/6x+6=34/9x-9 equation:

32/6x+6=34/9x-9

We move all terms to the left:

32/6x+6-(34/9x-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-34/9x+9+6=0

We calculate fractions


288x/54x^2+(-204x)/54x^2+9+6=0

We add all the numbers together, and all the variables

288x/54x^2+(-204x)/54x^2+15=0

We multiply all the terms by the denominator


288x+(-204x)+15*54x^2=0

Wy multiply elements

810x^2+288x+(-204x)=0

We get rid of parentheses

810x^2+288x-204x=0

We add all the numbers together, and all the variables

810x^2+84x=0

a = 810; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·810·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*810}=\frac{-168}{1620}
=-14/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*810}=\frac{0}{1620}
=0
$