5/3k+1/k=-2

Solution for 5/3k+1/k=-2 equation:

5/3k+1/k=-2

We move all terms to the left:

5/3k+1/k-(-2)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

5/3k+1/k+2=0

We calculate fractions


5k/3k^2+3k/3k^2+2=0

We multiply all the terms by the denominator


5k+3k+2*3k^2=0

We add all the numbers together, and all the variables

8k+2*3k^2=0

Wy multiply elements

6k^2+8k=0

a = 6; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·6·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*6}=\frac{-16}{12}
=-1+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*6}=\frac{0}{12}
=0
$