k/3k=6k+5-8k

Solution for k/3k=6k+5-8k equation:

k/3k=6k+5-8k

We move all terms to the left:

k/3k-(6k+5-8k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

k/3k+2k-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

6k^2+k-15k=0

We add all the numbers together, and all the variables

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