16=9/x^2

Solution for 16=9/x^2 equation:

16=9/x^2

We move all terms to the left:

16-(9/x^2)=0


Domain of the equation: x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-9/x^2+16=0

We multiply all the terms by the denominator


16*x^2-9=0

We add all the numbers together, and all the variables

16x^2-9=0

a = 16; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·16·(-9)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*16}=\frac{-24}{32}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*16}=\frac{24}{32}
=3/4
$