0=-24+k^2-k

Solution for 0=-24+k^2-k equation:

0=-24+k^2-k

We move all terms to the left:

0-(-24+k^2-k)=0

We add all the numbers together, and all the variables

-(-24+k^2-k)=0

We get rid of parentheses

-k^2+k+24=0

We add all the numbers together, and all the variables

-1k^2+k+24=0

a = -1; b = 1; c = +24;
Δ = b2-4ac
Δ = 12-4·(-1)·24
Δ = 97
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{-(1)-\sqrt{97}}{2*-1}=\frac{-1-\sqrt{97}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-1}=\frac{-1+\sqrt{97}}{-2}
$