1/2k-6=-1/6k

Solution for 1/2k-6=-1/6k equation:

1/2k-6=-1/6k

We move all terms to the left:

1/2k-6-(-1/6k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We get rid of parentheses

1/2k+1/6k-6=0

We calculate fractions


6k/12k^2+2k/12k^2-6=0

We multiply all the terms by the denominator


6k+2k-6*12k^2=0

We add all the numbers together, and all the variables

8k-6*12k^2=0

Wy multiply elements

-72k^2+8k=0

a = -72; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-72)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-72}=\frac{-16}{-144}
=1/9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-72}=\frac{0}{-144}
=0
$