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9k(7k+4)=9k+11
We move all terms to the left:
9k(7k+4)-(9k+11)=0
We multiply parentheses
63k^2+36k-(9k+11)=0
We get rid of parentheses
63k^2+36k-9k-11=0
We add all the numbers together, and all the variables
63k^2+27k-11=0
a = 63; b = 27; c = -11;
Δ = b2-4ac
Δ = 272-4·63·(-11)
Δ = 3501
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3501}=\sqrt{9*389}=\sqrt{9}*\sqrt{389}=3\sqrt{389}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{389}}{2*63}=\frac{-27-3\sqrt{389}}{126} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{389}}{2*63}=\frac{-27+3\sqrt{389}}{126} $
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