x(0.5x+6)=432

Solution for x(0.5x+6)=432 equation:

x(0.5x+6)=432

We move all terms to the left:

x(0.5x+6)-(432)=0

We multiply parentheses

0x^2+6x-432=0

We add all the numbers together, and all the variables

x^2+6x-432=0

a = 1; b = 6; c = -432;
Δ = b2-4ac
Δ = 62-4·1·(-432)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*1}=\frac{36}{2}
=18
$