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2/3k+1/2k=22
We move all terms to the left:
2/3k+1/2k-(22)=0
Domain of the equation: 3k!=0
k!=0/3
k!=0
k∈R
Domain of the equation: 2k!=0We calculate fractions
k!=0/2
k!=0
k∈R
4k/6k^2+3k/6k^2-22=0
We multiply all the terms by the denominator
4k+3k-22*6k^2=0
We add all the numbers together, and all the variables
7k-22*6k^2=0
Wy multiply elements
-132k^2+7k=0
a = -132; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-132)·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$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-132}=\frac{-14}{-264} =7/132 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-132}=\frac{0}{-264} =0 $
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