-7k(k+5)=0

Solution for -7k(k+5)=0 equation:

-7k(k+5)=0

We multiply parentheses

-7k^2-35k=0

a = -7; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-7)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-7}=\frac{0}{-14}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-7}=\frac{70}{-14}
=-5
$