5k^2+21=22k

Solution for 5k^2+21=22k equation:

5k^2+21=22k

We move all terms to the left:

5k^2+21-(22k)=0

a = 5; b = -22; c = +21;
Δ = b2-4ac
Δ = -222-4·5·21
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8}{2*5}=\frac{14}{10}
=1+2/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8}{2*5}=\frac{30}{10}
=3
$