6/9x+8=3/x-3

Solution for 6/9x+8=3/x-3 equation:

6/9x+8=3/x-3

We move all terms to the left:

6/9x+8-(3/x-3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

6/9x-3/x+3+8=0

We calculate fractions


6x/9x^2+(-27x)/9x^2+3+8=0

We add all the numbers together, and all the variables

6x/9x^2+(-27x)/9x^2+11=0

We multiply all the terms by the denominator


6x+(-27x)+11*9x^2=0

Wy multiply elements

99x^2+6x+(-27x)=0

We get rid of parentheses

99x^2+6x-27x=0

We add all the numbers together, and all the variables

99x^2-21x=0

a = 99; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·99·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*99}=\frac{0}{198}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*99}=\frac{42}{198}
=7/33
$