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8/9k-2/3=5+3/7k
We move all terms to the left:
8/9k-2/3-(5+3/7k)=0
Domain of the equation: 9k!=0
k!=0/9
k!=0
k∈R
Domain of the equation: 7k)!=0We add all the numbers together, and all the variables
k!=0/1
k!=0
k∈R
8/9k-(3/7k+5)-2/3=0
We get rid of parentheses
8/9k-3/7k-5-2/3=0
We calculate fractions
(-882k^2)/567k^2+504k/567k^2+(-243k)/567k^2-5=0
We multiply all the terms by the denominator
(-882k^2)+504k+(-243k)-5*567k^2=0
Wy multiply elements
(-882k^2)-2835k^2+504k+(-243k)=0
We get rid of parentheses
-882k^2-2835k^2+504k-243k=0
We add all the numbers together, and all the variables
-3717k^2+261k=0
a = -3717; b = 261; c = 0;
Δ = b2-4ac
Δ = 2612-4·(-3717)·0
Δ = 68121
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{68121}=261$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(261)-261}{2*-3717}=\frac{-522}{-7434} =29/413 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(261)+261}{2*-3717}=\frac{0}{-7434} =0 $
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