3/8*z,z=16

Solution for 3/8*z,z=16 equation:

3/8*z.z=16

We move all terms to the left:

3/8*z.z-(16)=0


Domain of the equation: 8*z.z!=0

z!=0/1

z!=0

z∈R


We multiply all the terms by the denominator


-16*8*z.z+3=0

Wy multiply elements

-128z*z+3=0

Wy multiply elements

-128z^2+3=0

a = -128; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-128)·3
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*-128}=\frac{0-16\sqrt{6}}{-256}
=-\frac{16\sqrt{6}}{-256}
=-\frac{\sqrt{6}}{-16}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*-128}=\frac{0+16\sqrt{6}}{-256}
=\frac{16\sqrt{6}}{-256}
=\frac{\sqrt{6}}{-16}
$