-2/3x+9=4/x-3

Solution for -2/3x+9=4/x-3 equation:

-2/3x+9=4/x-3

We move all terms to the left:

-2/3x+9-(4/x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

-2/3x-4/x+3+9=0

We calculate fractions


(-2x)/3x^2+(-12x)/3x^2+3+9=0

We add all the numbers together, and all the variables

(-2x)/3x^2+(-12x)/3x^2+12=0

We multiply all the terms by the denominator


(-2x)+(-12x)+12*3x^2=0

Wy multiply elements

36x^2+(-2x)+(-12x)=0

We get rid of parentheses

36x^2-2x-12x=0

We add all the numbers together, and all the variables

36x^2-14x=0

a = 36; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·36·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*36}=\frac{28}{72}
=7/18
$