432=x(.5x+6)

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

432=x(.5x+6)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(.5x+6)), so:

x(.5x+6)

We multiply parentheses

x^2+6x

Back to the equation:

-(x^2+6x)


We get rid of parentheses

-x^2-6x+432=0

We add all the numbers together, and all the variables

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