(X-6)(x+19)=0

Solution for (X-6)(x+19)=0 equation:

(X-6)(X+19)=0

We multiply parentheses ..

(+X^2+19X-6X-114)=0

We get rid of parentheses

X^2+19X-6X-114=0

We add all the numbers together, and all the variables

X^2+13X-114=0

a = 1; b = 13; c = -114;
Δ = b2-4ac
Δ = 132-4·1·(-114)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-25}{2*1}=\frac{-38}{2}
=-19
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+25}{2*1}=\frac{12}{2}
=6
$