4k^2-20=k

Solution for 4k^2-20=k equation:

4k^2-20=k

We move all terms to the left:

4k^2-20-(k)=0

We add all the numbers together, and all the variables

4k^2-1k-20=0

a = 4; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·4·(-20)
Δ = 321
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{321}}{2*4}=\frac{1-\sqrt{321}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{321}}{2*4}=\frac{1+\sqrt{321}}{8}
$