24/5k+4=4/k-1

Solution for 24/5k+4=4/k-1 equation:

24/5k+4=4/k-1

We move all terms to the left:

24/5k+4-(4/k-1)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



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

k∈R


We get rid of parentheses

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

We calculate fractions


24k/5k^2+(-20k)/5k^2+1+4=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

25k^2+24k+(-20k)=0

We get rid of parentheses

25k^2+24k-20k=0

We add all the numbers together, and all the variables

25k^2+4k=0

a = 25; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·25·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*25}=\frac{-8}{50}
=-4/25
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*25}=\frac{0}{50}
=0
$