-5k^2-4k-6=-7

Solution for -5k^2-4k-6=-7 equation:

-5k^2-4k-6=-7

We move all terms to the left:

-5k^2-4k-6-(-7)=0

We add all the numbers together, and all the variables

-5k^2-4k+1=0

a = -5; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-5)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*-5}=\frac{-2}{-10}
=1/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*-5}=\frac{10}{-10}
=-1
$