9x=16/x

Solution for 9x=16/x equation:

9x=16/x

We move all terms to the left:

9x-(16/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+16/x)=0

We get rid of parentheses

9x-16/x=0

We multiply all the terms by the denominator


9x*x-16=0

Wy multiply elements

9x^2-16=0

a = 9; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·9·(-16)
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*9}=\frac{-24}{18}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*9}=\frac{24}{18}
=1+1/3
$