7k(-k+-6)+2k=22

Solution for 7k(-k+-6)+2k=22 equation:

7k(-k+-6)+2k=22

We move all terms to the left:

7k(-k+-6)+2k-(22)=0

We add all the numbers together, and all the variables

7k(-1k-6)+2k-22=0

We add all the numbers together, and all the variables

2k+7k(-1k-6)-22=0

We multiply parentheses

-7k^2+2k-42k-22=0

We add all the numbers together, and all the variables

-7k^2-40k-22=0

a = -7; b = -40; c = -22;
Δ = b2-4ac
Δ = -402-4·(-7)·(-22)
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{246}}{2*-7}=\frac{40-2\sqrt{246}}{-14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{246}}{2*-7}=\frac{40+2\sqrt{246}}{-14}
$