0=22k-k^2-21

Solution for 0=22k-k^2-21 equation:

0=22k-k^2-21

We move all terms to the left:

0-(22k-k^2-21)=0

We add all the numbers together, and all the variables

-(22k-k^2-21)=0

We get rid of parentheses

k^2-22k+21=0

a = 1; b = -22; c = +21;
Δ = b2-4ac
Δ = -222-4·1·21
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-20}{2*1}=\frac{2}{2}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+20}{2*1}=\frac{42}{2}
=21
$