1/z=2z

Solution for 1/z=2z equation:

1/z=2z

We move all terms to the left:

1/z-(2z)=0


Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

-2z+1/z=0

We multiply all the terms by the denominator


-2z*z+1=0

Wy multiply elements

-2z^2+1=0

a = -2; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-2)·1
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-2}=\frac{0-2\sqrt{2}}{-4}
=-\frac{2\sqrt{2}}{-4}
=-\frac{\sqrt{2}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-2}=\frac{0+2\sqrt{2}}{-4}
=\frac{2\sqrt{2}}{-4}
=\frac{\sqrt{2}}{-2}
$