8/3k+2/k=-2

Solution for 8/3k+2/k=-2 equation:

8/3k+2/k=-2

We move all terms to the left:

8/3k+2/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

8/3k+2/k+2=0

We calculate fractions


8k/3k^2+6k/3k^2+2=0

We multiply all the terms by the denominator


8k+6k+2*3k^2=0

We add all the numbers together, and all the variables

14k+2*3k^2=0

Wy multiply elements

6k^2+14k=0

a = 6; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·6·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*6}=\frac{-28}{12}
=-2+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*6}=\frac{0}{12}
=0
$