x(x+19)-11(x+19)=0

Solution for x(x+19)-11(x+19)=0 equation:

x(x+19)-11(x+19)=0

We multiply parentheses

x^2+19x-11x-209=0

We add all the numbers together, and all the variables

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