9+3/x^2=45

Solution for 9+3/x^2=45 equation:

9+3/x^2=45

We move all terms to the left:

9+3/x^2-(45)=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

3/x^2-36=0

We multiply all the terms by the denominator


-36*x^2+3=0

We add all the numbers together, and all the variables

-36x^2+3=0

a = -36; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-36)·3
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*-36}=\frac{0-12\sqrt{3}}{-72}
=-\frac{12\sqrt{3}}{-72}
=-\frac{\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-36}=\frac{0+12\sqrt{3}}{-72}
=\frac{12\sqrt{3}}{-72}
=\frac{\sqrt{3}}{-6}
$