z+2/z=-6

Solution for z+2/z=-6 equation:

z+2/z=-6

We move all terms to the left:

z+2/z-(-6)=0


Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

z+2/z+6=0

We multiply all the terms by the denominator


z*z+6*z+2=0

We add all the numbers together, and all the variables

6z+z*z+2=0

Wy multiply elements

z^2+6z+2=0

a = 1; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·1·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*1}=\frac{-6-2\sqrt{7}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*1}=\frac{-6+2\sqrt{7}}{2}
$