0=x^2+8x-209

Solution for 0=x^2+8x-209 equation:

0=x^2+8x-209

We move all terms to the left:

0-(x^2+8x-209)=0

We add all the numbers together, and all the variables

-(x^2+8x-209)=0

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
$