5k^2=-10k

Solution for 5k^2=-10k equation:

5k^2=-10k

We move all terms to the left:

5k^2-(-10k)=0

We get rid of parentheses

5k^2+10k=0

a = 5; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·5·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*5}=\frac{-20}{10}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*5}=\frac{0}{10}
=0
$