85=w*(w+12)

Solution for 85=w*(w+12) equation:

85=w(w+12)

We move all terms to the left:

85-(w(w+12))=0


We calculate terms in parentheses: -(w(w+12)), so:

w(w+12)

We multiply parentheses

w^2+12w

Back to the equation:

-(w^2+12w)


We get rid of parentheses

-w^2-12w+85=0

We add all the numbers together, and all the variables

-1w^2-12w+85=0

a = -1; b = -12; c = +85;
Δ = b2-4ac
Δ = -122-4·(-1)·85
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-22}{2*-1}=\frac{-10}{-2}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+22}{2*-1}=\frac{34}{-2}
=-17
$