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

Solution for ((2x)/(x-4))+((9)/(x+9))=0 equation:

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


Domain of the equation: (x-4))!=0

x∈R



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

x∈R


We calculate fractions


(2x^2+18x)/((x-4))*x+(9x-36)/((x-4))*x=0

We multiply all the terms by the denominator


(2x^2+18x)+(9x-36)=0

We get rid of parentheses

2x^2+18x+9x-36=0

We add all the numbers together, and all the variables

2x^2+27x-36=0

a = 2; b = 27; c = -36;
Δ = b2-4ac
Δ = 272-4·2·(-36)
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{113}}{2*2}=\frac{-27-3\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{113}}{2*2}=\frac{-27+3\sqrt{113}}{4}
$