x(x+24)-20(x+24)=0

Solution for x(x+24)-20(x+24)=0 equation:

x(x+24)-20(x+24)=0

We multiply parentheses

x^2+24x-20x-480=0

We add all the numbers together, and all the variables

x^2+4x-480=0

a = 1; b = 4; c = -480;
Δ = b2-4ac
Δ = 42-4·1·(-480)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-44}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+44}{2*1}=\frac{40}{2}
=20
$