85=w*(w+13)

Solution for 85=w*(w+13) equation:

85=w(w+13)

We move all terms to the left:

85-(w(w+13))=0


We calculate terms in parentheses: -(w(w+13)), so:

w(w+13)

We multiply parentheses

w^2+13w

Back to the equation:

-(w^2+13w)


We get rid of parentheses

-w^2-13w+85=0

We add all the numbers together, and all the variables

-1w^2-13w+85=0

a = -1; b = -13; c = +85;
Δ = b2-4ac
Δ = -132-4·(-1)·85
Δ = 509
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{509}}{2*-1}=\frac{13-\sqrt{509}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{509}}{2*-1}=\frac{13+\sqrt{509}}{-2}
$