(4)(k)(k-6)=0

Solution for (4)(k)(k-6)=0 equation:

(4)(k)(k-6)=0

We multiply parentheses

4k^2-24k=0

a = 4; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·4·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*4}=\frac{0}{8}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*4}=\frac{48}{8}
=6
$