X(x-8)=209

Solution for X(x-8)=209 equation:

X(X-8)=209

We move all terms to the left:

X(X-8)-(209)=0

We multiply parentheses

X^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
$