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2/7k-1/14k=13
We move all terms to the left:
2/7k-1/14k-(13)=0
Domain of the equation: 7k!=0
k!=0/7
k!=0
k∈R
Domain of the equation: 14k!=0We calculate fractions
k!=0/14
k!=0
k∈R
28k/98k^2+(-7k)/98k^2-13=0
We multiply all the terms by the denominator
28k+(-7k)-13*98k^2=0
Wy multiply elements
-1274k^2+28k+(-7k)=0
We get rid of parentheses
-1274k^2+28k-7k=0
We add all the numbers together, and all the variables
-1274k^2+21k=0
a = -1274; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-1274)·0
Δ = 441
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{441}=21$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-1274}=\frac{-42}{-2548} =3/182 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-1274}=\frac{0}{-2548} =0 $
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