-108(x^2-3)/(x^2+9)^3=0

Solution for -108(x^2-3)/(x^2+9)^3=0 equation:

-108(x^2-3)/(x^2+9)^3=0


Domain of the equation: (x^2+9)^3!=0

x∈R


We multiply all the terms by the denominator


-108(x^2-3)=0

We multiply parentheses

-108x^2+324=0

a = -108; b = 0; c = +324;
Δ = b2-4ac
Δ = 02-4·(-108)·324
Δ = 139968
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:

$\sqrt{\Delta}=\sqrt{139968}=\sqrt{46656*3}=\sqrt{46656}*\sqrt{3}=216\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-216\sqrt{3}}{2*-108}=\frac{0-216\sqrt{3}}{-216}
=-\frac{216\sqrt{3}}{-216}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+216\sqrt{3}}{2*-108}=\frac{0+216\sqrt{3}}{-216}
=\frac{216\sqrt{3}}{-216}
=\frac{\sqrt{3}}{-1}
$