-7/12k-84=k

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}
$