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

Solution for -3(4x^2-3)/(2(4x^2+3)^2)=0 equation:

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


Domain of the equation: (2(4x^2+3)^2)!=0

x∈R


We multiply all the terms by the denominator


-3(4x^2-3)=0

We multiply parentheses

-12x^2+9=0

a = -12; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-12)·9
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-12}=\frac{0-12\sqrt{3}}{-24}
=-\frac{12\sqrt{3}}{-24}
=-\frac{\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-12}=\frac{0+12\sqrt{3}}{-24}
=\frac{12\sqrt{3}}{-24}
=\frac{\sqrt{3}}{-2}
$