-4k-7k-9=-2k-6k^2-2

Solution for -4k-7k-9=-2k-6k^2-2 equation:

-4k-7k-9=-2k-6k^2-2

We move all terms to the left:

-4k-7k-9-(-2k-6k^2-2)=0

We add all the numbers together, and all the variables

-(-2k-6k^2-2)-11k-9=0

We get rid of parentheses

6k^2+2k-11k+2-9=0

We add all the numbers together, and all the variables

6k^2-9k-7=0

a = 6; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·6·(-7)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{249}}{2*6}=\frac{9-\sqrt{249}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{249}}{2*6}=\frac{9+\sqrt{249}}{12}
$