4k2=-k

Solution for 4k2=-k equation:

4k^2=-k

We move all terms to the left:

4k^2-(-k)=0

We add all the numbers together, and all the variables

4k^2-(-1k)=0

We get rid of parentheses

4k^2+1k=0

We add all the numbers together, and all the variables

4k^2+k=0

a = 4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·4·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*4}=\frac{-2}{8}
=-1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*4}=\frac{0}{8}
=0
$