4k(k+10)=0

Solution for 4k(k+10)=0 equation:

4k(k+10)=0

We multiply parentheses

4k^2+40k=0

a = 4; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·4·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*4}=\frac{-80}{8}
=-10
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*4}=\frac{0}{8}
=0
$