-7/12k-84=k

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Solution for -7/12k-84=k equation:



-7/12k-84=k
We move all terms to the left:
-7/12k-84-(k)=0
Domain of the equation: 12k!=0
k!=0/12
k!=0
k∈R
We add all the numbers together, and all the variables
-1k-7/12k-84=0
We multiply all the terms by the denominator
-1k*12k-84*12k-7=0
Wy multiply elements
-12k^2-1008k-7=0
a = -12; b = -1008; c = -7;
Δ = b2-4ac
Δ = -10082-4·(-12)·(-7)
Δ = 1015728
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:
$\sqrt{\Delta}=\sqrt{1015728}=\sqrt{16*63483}=\sqrt{16}*\sqrt{63483}=4\sqrt{63483}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-4\sqrt{63483}}{2*-12}=\frac{1008-4\sqrt{63483}}{-24} $
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+4\sqrt{63483}}{2*-12}=\frac{1008+4\sqrt{63483}}{-24} $

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