(16-48x^2)/(1+x^2)^3=0

Solution for (16-48x^2)/(1+x^2)^3=0 equation:

(16-48x^2)/(1+x^2)^3=0


Domain of the equation: (1+x^2)^3!=0

x∈R


We multiply all the terms by the denominator


(16-48x^2)=0

We get rid of parentheses

-48x^2+16=0

a = -48; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-48)·16
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*-48}=\frac{0-32\sqrt{3}}{-96}
=-\frac{32\sqrt{3}}{-96}
=-\frac{\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*-48}=\frac{0+32\sqrt{3}}{-96}
=\frac{32\sqrt{3}}{-96}
=\frac{\sqrt{3}}{-3}
$