55=w(6+w)

Solution for 55=w(6+w) equation:

55=w(6+w)

We move all terms to the left:

55-(w(6+w))=0

We add all the numbers together, and all the variables

-(w(w+6))+55=0


We calculate terms in parentheses: -(w(w+6)), so:

w(w+6)

We multiply parentheses

w^2+6w

Back to the equation:

-(w^2+6w)


We get rid of parentheses

-w^2-6w+55=0

We add all the numbers together, and all the variables

-1w^2-6w+55=0

a = -1; b = -6; c = +55;
Δ = b2-4ac
Δ = -62-4·(-1)·55
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-16}{2*-1}=\frac{-10}{-2}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+16}{2*-1}=\frac{22}{-2}
=-11
$