(x+19)(x-20)=0

Solution for (x+19)(x-20)=0 equation:

(x+19)(x-20)=0

We multiply parentheses ..

(+x^2-20x+19x-380)=0

We get rid of parentheses

x^2-20x+19x-380=0

We add all the numbers together, and all the variables

x^2-1x-380=0

a = 1; b = -1; c = -380;
Δ = b2-4ac
Δ = -12-4·1·(-380)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-39}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+39}{2*1}=\frac{40}{2}
=20
$