432=(1/2w+6)w

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

432=(1/2w+6)w

We move all terms to the left:

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


Domain of the equation: 2w+6)w)!=0

w∈R


We multiply all the terms by the denominator


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


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

(1+432*2w+6)w

We add all the numbers together, and all the variables

(432*2w+7)w

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
$