324=w(w+15)

Solution for 324=w(w+15) equation:

324=w(w+15)

We move all terms to the left:

324-(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+324=0

We add all the numbers together, and all the variables

-1w^2-15w+324=0

a = -1; b = -15; c = +324;
Δ = b2-4ac
Δ = -152-4·(-1)·324
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-39}{2*-1}=\frac{-24}{-2}
=+12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+39}{2*-1}=\frac{54}{-2}
=-27
$