16=-2k(k+9)

Solution for 16=-2k(k+9) equation:

16=-2k(k+9)

We move all terms to the left:

16-(-2k(k+9))=0


We calculate terms in parentheses: -(-2k(k+9)), so:

-2k(k+9)

We multiply parentheses

-2k^2-18k

Back to the equation:

-(-2k^2-18k)


We get rid of parentheses

2k^2+18k+16=0

a = 2; b = 18; c = +16;
Δ = b2-4ac
Δ = 182-4·2·16
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-14}{2*2}=\frac{-32}{4}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+14}{2*2}=\frac{-4}{4}
=-1
$