5k(k+7)=0

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

5k(k+7)=0

We multiply parentheses

5k^2+35k=0

a = 5; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·5·0
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*5}=\frac{-70}{10}
=-7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*5}=\frac{0}{10}
=0
$