w(w+16)=35

Solution for w(w+16)=35 equation:

w(w+16)=35

We move all terms to the left:

w(w+16)-(35)=0

We multiply parentheses

w^2+16w-35=0

a = 1; b = 16; c = -35;
Δ = b2-4ac
Δ = 162-4·1·(-35)
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-6\sqrt{11}}{2*1}=\frac{-16-6\sqrt{11}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+6\sqrt{11}}{2*1}=\frac{-16+6\sqrt{11}}{2}
$