-k^2-3k-2=-5k^2

Solution for -k^2-3k-2=-5k^2 equation:

-k^2-3k-2=-5k^2

We move all terms to the left:

-k^2-3k-2-(-5k^2)=0

We add all the numbers together, and all the variables

-1k^2-(-5k^2)-3k-2=0

We get rid of parentheses

-1k^2+5k^2-3k-2=0

We add all the numbers together, and all the variables

4k^2-3k-2=0

a = 4; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·4·(-2)
Δ = 41
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{-(-3)-\sqrt{41}}{2*4}=\frac{3-\sqrt{41}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*4}=\frac{3+\sqrt{41}}{8}
$