z-6/z=-8

Solution for z-6/z=-8 equation:

z-6/z=-8

We move all terms to the left:

z-6/z-(-8)=0


Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

z-6/z+8=0

We multiply all the terms by the denominator


z*z+8*z-6=0

We add all the numbers together, and all the variables

8z+z*z-6=0

Wy multiply elements

z^2+8z-6=0

a = 1; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·1·(-6)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*1}=\frac{-8-2\sqrt{22}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*1}=\frac{-8+2\sqrt{22}}{2}
$