260=w*(16+w)

Solution for 260=w*(16+w) equation:

260=w(16+w)

We move all terms to the left:

260-(w(16+w))=0

We add all the numbers together, and all the variables

-(w(w+16))+260=0


We calculate terms in parentheses: -(w(w+16)), so:

w(w+16)

We multiply parentheses

w^2+16w

Back to the equation:

-(w^2+16w)


We get rid of parentheses

-w^2-16w+260=0

We add all the numbers together, and all the variables

-1w^2-16w+260=0

a = -1; b = -16; c = +260;
Δ = b2-4ac
Δ = -162-4·(-1)·260
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-36}{2*-1}=\frac{-20}{-2}
=+10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+36}{2*-1}=\frac{52}{-2}
=-26
$