5z+z=24/z

Solution for 5z+z=24/z equation:

5z+z=24/z

We move all terms to the left:

5z+z-(24/z)=0


Domain of the equation: z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

5z+z-(+24/z)=0

We add all the numbers together, and all the variables

6z-(+24/z)=0

We get rid of parentheses

6z-24/z=0

We multiply all the terms by the denominator


6z*z-24=0

Wy multiply elements

6z^2-24=0

a = 6; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·6·(-24)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*6}=\frac{-24}{12}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*6}=\frac{24}{12}
=2
$