(x+19)(x-24)=0

Solution for (x+19)(x-24)=0 equation:

(x+19)(x-24)=0

We multiply parentheses ..

(+x^2-24x+19x-456)=0

We get rid of parentheses

x^2-24x+19x-456=0

We add all the numbers together, and all the variables

x^2-5x-456=0

a = 1; b = -5; c = -456;
Δ = b2-4ac
Δ = -52-4·1·(-456)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-43}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+43}{2*1}=\frac{48}{2}
=24
$