84=w(w+8)

Solution for 84=w(w+8) equation:

84=w(w+8)

We move all terms to the left:

84-(w(w+8))=0


We calculate terms in parentheses: -(w(w+8)), so:

w(w+8)

We multiply parentheses

w^2+8w

Back to the equation:

-(w^2+8w)


We get rid of parentheses

-w^2-8w+84=0

We add all the numbers together, and all the variables

-1w^2-8w+84=0

a = -1; b = -8; c = +84;
Δ = b2-4ac
Δ = -82-4·(-1)·84
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*-1}=\frac{-12}{-2}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*-1}=\frac{28}{-2}
=-14
$