(x-2)(x+19)=0

Solution for (x-2)(x+19)=0 equation:

(x-2)(x+19)=0

We multiply parentheses ..

(+x^2+19x-2x-38)=0

We get rid of parentheses

x^2+19x-2x-38=0

We add all the numbers together, and all the variables

x^2+17x-38=0

a = 1; b = 17; c = -38;
Δ = b2-4ac
Δ = 172-4·1·(-38)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-21}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+21}{2*1}=\frac{4}{2}
=2
$