(w-13)*(w-13)-16=0

Solution for (w-13)*(w-13)-16=0 equation:

(w-13)(w-13)-16=0

We multiply parentheses ..

(+w^2-13w-13w+169)-16=0

We get rid of parentheses

w^2-13w-13w+169-16=0

We add all the numbers together, and all the variables

w^2-26w+153=0

a = 1; b = -26; c = +153;
Δ = b2-4ac
Δ = -262-4·1·153
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-8}{2*1}=\frac{18}{2}
=9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+8}{2*1}=\frac{34}{2}
=17
$