(x-19)(x+13)=0

Solution for (x-19)(x+13)=0 equation:

(x-19)(x+13)=0

We multiply parentheses ..

(+x^2+13x-19x-247)=0

We get rid of parentheses

x^2+13x-19x-247=0

We add all the numbers together, and all the variables

x^2-6x-247=0

a = 1; b = -6; c = -247;
Δ = b2-4ac
Δ = -62-4·1·(-247)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-32}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+32}{2*1}=\frac{38}{2}
=19
$