0=k(k+9)

Solution for 0=k(k+9) equation:

0=k(k+9)

We move all terms to the left:

0-(k(k+9))=0

We add all the numbers together, and all the variables

-(k(k+9))=0


We calculate terms in parentheses: -(k(k+9)), so:

k(k+9)

We multiply parentheses

k^2+9k

Back to the equation:

-(k^2+9k)


We get rid of parentheses

-k^2-9k=0

We add all the numbers together, and all the variables

-1k^2-9k=0

a = -1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-1}=\frac{0}{-2}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-1}=\frac{18}{-2}
=-9
$