3k-k/k=20-k/3k

Solution for 3k-k/k=20-k/3k equation:

3k-k/k=20-k/3k

We move all terms to the left:

3k-k/k-(20-k/3k)=0


Domain of the equation: k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3k-k/k-(-k/3k+20)=0

We get rid of parentheses

3k-k/k+k/3k-20=0

Fractions to decimals

k/3k+3k-20+1=0

We multiply all the terms by the denominator


k+3k*3k-20*3k+1*3k=0

Wy multiply elements

9k^2+k-60k+3k=0

We add all the numbers together, and all the variables

9k^2-56k=0

a = 9; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·9·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*9}=\frac{0}{18}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*9}=\frac{112}{18}
=6+2/9
$