432=w(6+1/2w)

Solution for 432=w(6+1/2w) equation:

432=w(6+1/2w)

We move all terms to the left:

432-(w(6+1/2w))=0


Domain of the equation: 2w))!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-(w(1/2w+6))+432=0

We multiply all the terms by the denominator


-(w(1+432*2w+6))=0


We calculate terms in parentheses: -(w(1+432*2w+6)), so:

w(1+432*2w+6)

We add all the numbers together, and all the variables

w(432*2w+7)

We multiply parentheses

864w^2+7w

Back to the equation:

-(864w^2+7w)


We get rid of parentheses

-864w^2-7w=0

a = -864; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-864)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-864}=\frac{0}{-1728}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-864}=\frac{14}{-1728}
=-7/864
$