X(6+.5x)=432

Solution for X(6+.5x)=432 equation:

X(6+.5X)=432

We move all terms to the left:

X(6+.5X)-(432)=0

We add all the numbers together, and all the variables

X(.5X+6)-432=0

We multiply parentheses

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
$