3=12/z2

Solution for 3=12/z2 equation:

3=12/z2

We move all terms to the left:

3-(12/z2)=0


Domain of the equation: z2)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-(+12/z2)+3=0

We get rid of parentheses

-12/z2+3=0

We multiply all the terms by the denominator


3*z2-12=0

We add all the numbers together, and all the variables

3z^2-12=0

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