w(w+8)=105

Solution for w(w+8)=105 equation:

w(w+8)=105

We move all terms to the left:

w(w+8)-(105)=0

We multiply parentheses

w^2+8w-105=0

a = 1; b = 8; c = -105;
Δ = b2-4ac
Δ = 82-4·1·(-105)
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{-(8)-22}{2*1}=\frac{-30}{2}
=-15
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*1}=\frac{14}{2}
=7
$