x(x-24)=432

Solution for x(x-24)=432 equation:

x(x-24)=432

We move all terms to the left:

x(x-24)-(432)=0

We multiply parentheses

x^2-24x-432=0

a = 1; b = -24; c = -432;
Δ = b2-4ac
Δ = -242-4·1·(-432)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-48}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+48}{2*1}=\frac{72}{2}
=36
$