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1/2k+1/5k=1
We move all terms to the left:
1/2k+1/5k-(1)=0
Domain of the equation: 2k!=0
k!=0/2
k!=0
k∈R
Domain of the equation: 5k!=0We calculate fractions
k!=0/5
k!=0
k∈R
5k/10k^2+2k/10k^2-1=0
We multiply all the terms by the denominator
5k+2k-1*10k^2=0
We add all the numbers together, and all the variables
7k-1*10k^2=0
Wy multiply elements
-10k^2+7k=0
a = -10; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-10)·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$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-10}=\frac{-14}{-20} =7/10 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-10}=\frac{0}{-20} =0 $
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