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1/3k+4=5/6k-12
We move all terms to the left:
1/3k+4-(5/6k-12)=0
Domain of the equation: 3k!=0
k!=0/3
k!=0
k∈R
Domain of the equation: 6k-12)!=0We get rid of parentheses
k∈R
1/3k-5/6k+12+4=0
We calculate fractions
6k/18k^2+(-15k)/18k^2+12+4=0
We add all the numbers together, and all the variables
6k/18k^2+(-15k)/18k^2+16=0
We multiply all the terms by the denominator
6k+(-15k)+16*18k^2=0
Wy multiply elements
288k^2+6k+(-15k)=0
We get rid of parentheses
288k^2+6k-15k=0
We add all the numbers together, and all the variables
288k^2-9k=0
a = 288; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·288·0
Δ = 81
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{81}=9$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*288}=\frac{0}{576} =0 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*288}=\frac{18}{576} =1/32 $
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