207=k(k+3)

Solution for 207=k(k+3) equation:

207=k(k+3)

We move all terms to the left:

207-(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+207=0

We add all the numbers together, and all the variables

-1k^2-3k+207=0

a = -1; b = -3; c = +207;
Δ = b2-4ac
Δ = -32-4·(-1)·207
Δ = 837
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{93}}{2*-1}=\frac{3-3\sqrt{93}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{93}}{2*-1}=\frac{3+3\sqrt{93}}{-2}
$