24/5z=4/z-1

Solution for 24/5z=4/z-1 equation:

24/5z=4/z-1

We move all terms to the left:

24/5z-(4/z-1)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: z-1)!=0

z∈R


We get rid of parentheses

24/5z-4/z+1=0

We calculate fractions


24z/5z^2+(-20z)/5z^2+1=0

We multiply all the terms by the denominator


24z+(-20z)+1*5z^2=0

Wy multiply elements

5z^2+24z+(-20z)=0

We get rid of parentheses

5z^2+24z-20z=0

We add all the numbers together, and all the variables

5z^2+4z=0

a = 5; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·5·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*5}=\frac{-8}{10}
=-4/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*5}=\frac{0}{10}
=0
$