9z=4/z

Solution for 9z=4/z equation:

9z=4/z

We move all terms to the left:

9z-(4/z)=0


Domain of the equation: z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

9z-(+4/z)=0

We get rid of parentheses

9z-4/z=0

We multiply all the terms by the denominator


9z*z-4=0

Wy multiply elements

9z^2-4=0

a = 9; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·9·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*9}=\frac{-12}{18}
=-2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*9}=\frac{12}{18}
=2/3
$