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

Solution for -(4(x^2-6))/((x^2+6)^2)=0 equation:

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


Domain of the equation: ((x^2+6)^2)!=0

x∈R


We multiply all the terms by the denominator


-(4(x^2-6))=0


We calculate terms in parentheses: -(4(x^2-6)), so:

4(x^2-6)

We multiply parentheses

4x^2-24

Back to the equation:

-(4x^2-24)


We get rid of parentheses

-4x^2+24=0

a = -4; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-4)·24
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-4}=\frac{0-8\sqrt{6}}{-8}
=-\frac{8\sqrt{6}}{-8}
=-\frac{\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-4}=\frac{0+8\sqrt{6}}{-8}
=\frac{8\sqrt{6}}{-8}
=\frac{\sqrt{6}}{-1}
$