8k-1/3k=5k

Solution for 8k-1/3k=5k equation:

8k-1/3k=5k

We move all terms to the left:

8k-1/3k-(5k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

3k-1/3k=0

We multiply all the terms by the denominator


3k*3k-1=0

Wy multiply elements

9k^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$