4+4k+4k^2=21k

Solution for 4+4k+4k^2=21k equation:

4+4k+4k^2=21k

We move all terms to the left:

4+4k+4k^2-(21k)=0

We add all the numbers together, and all the variables

4k^2-17k+4=0

a = 4; b = -17; c = +4;
Δ = b2-4ac
Δ = -172-4·4·4
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-15}{2*4}=\frac{2}{8}
=1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+15}{2*4}=\frac{32}{8}
=4
$