z+6/z=-7

Solution for z+6/z=-7 equation:

z+6/z=-7

We move all terms to the left:

z+6/z-(-7)=0


Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

z+6/z+7=0

We multiply all the terms by the denominator


z*z+7*z+6=0

We add all the numbers together, and all the variables

7z+z*z+6=0

Wy multiply elements

z^2+7z+6=0

a = 1; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*1}=\frac{-12}{2}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*1}=\frac{-2}{2}
=-1
$