54=w(3+2w)

Solution for 54=w(3+2w) equation:

54=w(3+2w)

We move all terms to the left:

54-(w(3+2w))=0

We add all the numbers together, and all the variables

-(w(2w+3))+54=0


We calculate terms in parentheses: -(w(2w+3)), so:

w(2w+3)

We multiply parentheses

2w^2+3w

Back to the equation:

-(2w^2+3w)


We get rid of parentheses

-2w^2-3w+54=0

a = -2; b = -3; c = +54;
Δ = b2-4ac
Δ = -32-4·(-2)·54
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*-2}=\frac{24}{-4}
=-6
$