(x+19)(x-16)=0

Solution for (x+19)(x-16)=0 equation:

(x+19)(x-16)=0

We multiply parentheses ..

(+x^2-16x+19x-304)=0

We get rid of parentheses

x^2-16x+19x-304=0

We add all the numbers together, and all the variables

x^2+3x-304=0

a = 1; b = 3; c = -304;
Δ = b2-4ac
Δ = 32-4·1·(-304)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-35}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+35}{2*1}=\frac{32}{2}
=16
$