20-8k/k-5=3k

Solution for 20-8k/k-5=3k equation:

20-8k/k-5=3k

We move all terms to the left:

20-8k/k-5-(3k)=0


Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

-3k-8k/k+15=0

We multiply all the terms by the denominator


-3k*k-8k+15*k=0

We add all the numbers together, and all the variables

7k-3k*k=0

Wy multiply elements

-3k^2+7k=0

a = -3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-3)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-3}=\frac{0}{-6}
=0
$