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

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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 $

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