208=k(k+3)

Solution for 208=k(k+3) equation:

208=k(k+3)

We move all terms to the left:

208-(k(k+3))=0


We calculate terms in parentheses: -(k(k+3)), so:

k(k+3)

We multiply parentheses

k^2+3k

Back to the equation:

-(k^2+3k)


We get rid of parentheses

-k^2-3k+208=0

We add all the numbers together, and all the variables

-1k^2-3k+208=0

a = -1; b = -3; c = +208;
Δ = b2-4ac
Δ = -32-4·(-1)·208
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-29}{2*-1}=\frac{-26}{-2}
=+13
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+29}{2*-1}=\frac{32}{-2}
=-16
$