w(w+2)=35^2

Solution for w(w+2)=35^2 equation:

w(w+2)=35^2

We move all terms to the left:

w(w+2)-(35^2)=0

We add all the numbers together, and all the variables

w(w+2)-1225=0

We multiply parentheses

w^2+2w-1225=0

a = 1; b = 2; c = -1225;
Δ = b2-4ac
Δ = 22-4·1·(-1225)
Δ = 4904
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:

$\sqrt{\Delta}=\sqrt{4904}=\sqrt{4*1226}=\sqrt{4}*\sqrt{1226}=2\sqrt{1226}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1226}}{2*1}=\frac{-2-2\sqrt{1226}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1226}}{2*1}=\frac{-2+2\sqrt{1226}}{2}
$