54=w(w+15)

Solution for 54=w(w+15) equation:

54=w(w+15)

We move all terms to the left:

54-(w(w+15))=0


We calculate terms in parentheses: -(w(w+15)), so:

w(w+15)

We multiply parentheses

w^2+15w

Back to the equation:

-(w^2+15w)


We get rid of parentheses

-w^2-15w+54=0

We add all the numbers together, and all the variables

-1w^2-15w+54=0

a = -1; b = -15; c = +54;
Δ = b2-4ac
Δ = -152-4·(-1)·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{-(-15)-21}{2*-1}=\frac{-6}{-2}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*-1}=\frac{36}{-2}
=-18
$