(x-7)(x-19)=0

Solution for (x-7)(x-19)=0 equation:

(x-7)(x-19)=0

We multiply parentheses ..

(+x^2-19x-7x+133)=0

We get rid of parentheses

x^2-19x-7x+133=0

We add all the numbers together, and all the variables

x^2-26x+133=0

a = 1; b = -26; c = +133;
Δ = b2-4ac
Δ = -262-4·1·133
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-12}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+12}{2*1}=\frac{38}{2}
=19
$