4/3z=8/z-5

Solution for 4/3z=8/z-5 equation:

4/3z=8/z-5

We move all terms to the left:

4/3z-(8/z-5)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R



Domain of the equation: z-5)!=0

z∈R


We get rid of parentheses

4/3z-8/z+5=0

We calculate fractions


4z/3z^2+(-24z)/3z^2+5=0

We multiply all the terms by the denominator


4z+(-24z)+5*3z^2=0

Wy multiply elements

15z^2+4z+(-24z)=0

We get rid of parentheses

15z^2+4z-24z=0

We add all the numbers together, and all the variables

15z^2-20z=0

a = 15; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·15·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*15}=\frac{0}{30}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*15}=\frac{40}{30}
=1+1/3
$