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k=7/9k=
We move all terms to the left:
k-(7/9k)=0
Domain of the equation: 9k)!=0We add all the numbers together, and all the variables
k!=0/1
k!=0
k∈R
k-(+7/9k)=0
We get rid of parentheses
k-7/9k=0
We multiply all the terms by the denominator
k*9k-7=0
Wy multiply elements
9k^2-7=0
a = 9; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·9·(-7)
Δ = 252
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*9}=\frac{0-6\sqrt{7}}{18} =-\frac{6\sqrt{7}}{18} =-\frac{\sqrt{7}}{3} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*9}=\frac{0+6\sqrt{7}}{18} =\frac{6\sqrt{7}}{18} =\frac{\sqrt{7}}{3} $
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