w(w+15)=82

Solution for w(w+15)=82 equation:

w(w+15)=82

We move all terms to the left:

w(w+15)-(82)=0

We multiply parentheses

w^2+15w-82=0

a = 1; b = 15; c = -82;
Δ = b2-4ac
Δ = 152-4·1·(-82)
Δ = 553
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{-(15)-\sqrt{553}}{2*1}=\frac{-15-\sqrt{553}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{553}}{2*1}=\frac{-15+\sqrt{553}}{2}
$