(72x^2+12-144x^2)/(6x^2+1)^2=0

Solution for (72x^2+12-144x^2)/(6x^2+1)^2=0 equation:

(72x^2+12-144x^2)/(6x^2+1)^2=0


Domain of the equation: (6x^2+1)^2!=0

x∈R


We multiply all the terms by the denominator


(72x^2+12-144x^2)=0

We get rid of parentheses

72x^2-144x^2+12=0

We add all the numbers together, and all the variables

-72x^2+12=0

a = -72; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-72)·12
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*-72}=\frac{0-24\sqrt{6}}{-144}
=-\frac{24\sqrt{6}}{-144}
=-\frac{\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*-72}=\frac{0+24\sqrt{6}}{-144}
=\frac{24\sqrt{6}}{-144}
=\frac{\sqrt{6}}{-6}
$