-2/x+4=6/3x-9

Solution for -2/x+4=6/3x-9 equation:

-2/x+4=6/3x-9

We move all terms to the left:

-2/x+4-(6/3x-9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-9)!=0

x∈R


We get rid of parentheses

-2/x-6/3x+9+4=0

We calculate fractions


(-6x)/3x^2+(-6x)/3x^2+9+4=0

We add all the numbers together, and all the variables

(-6x)/3x^2+(-6x)/3x^2+13=0

We multiply all the terms by the denominator


(-6x)+(-6x)+13*3x^2=0

Wy multiply elements

39x^2+(-6x)+(-6x)=0

We get rid of parentheses

39x^2-6x-6x=0

We add all the numbers together, and all the variables

39x^2-12x=0

a = 39; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·39·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*39}=\frac{0}{78}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*39}=\frac{24}{78}
=4/13
$