108/x^2+4=6

Solution for 108/x^2+4=6 equation:

108/x^2+4=6

We move all terms to the left:

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


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

108/x^2-2=0

We multiply all the terms by the denominator


-2*x^2+108=0

We add all the numbers together, and all the variables

-2x^2+108=0

a = -2; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-2)·108
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*-2}=\frac{0-12\sqrt{6}}{-4}
=-\frac{12\sqrt{6}}{-4}
=-\frac{3\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*-2}=\frac{0+12\sqrt{6}}{-4}
=\frac{12\sqrt{6}}{-4}
=\frac{3\sqrt{6}}{-1}
$