209=x(x+8)

Solution for 209=x(x+8) equation:

209=x(x+8)

We move all terms to the left:

209-(x(x+8))=0


We calculate terms in parentheses: -(x(x+8)), so:

x(x+8)

We multiply parentheses

x^2+8x

Back to the equation:

-(x^2+8x)


We get rid of parentheses

-x^2-8x+209=0

We add all the numbers together, and all the variables

-1x^2-8x+209=0

a = -1; b = -8; c = +209;
Δ = b2-4ac
Δ = -82-4·(-1)·209
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-30}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+30}{2*-1}=\frac{38}{-2}
=-19
$