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

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

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

We move all terms to the left:

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

10z^2+24z+(-5z)=0

We get rid of parentheses

10z^2+24z-5z=0

We add all the numbers together, and all the variables

10z^2+19z=0

a = 10; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·10·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*10}=\frac{-38}{20}
=-1+9/10
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*10}=\frac{0}{20}
=0
$