k^2=-17k

Solution for k^2=-17k equation:

k^2=-17k

We move all terms to the left:

k^2-(-17k)=0

We get rid of parentheses

k^2+17k=0

a = 1; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·1·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*1}=\frac{-34}{2}
=-17
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*1}=\frac{0}{2}
=0
$