(x-8)(x-8)-225=0

Solution for (x-8)(x-8)-225=0 equation:

(x-8)(x-8)-225=0

We multiply parentheses ..

(+x^2-8x-8x+64)-225=0

We get rid of parentheses

x^2-8x-8x+64-225=0

We add all the numbers together, and all the variables

x^2-16x-161=0

a = 1; b = -16; c = -161;
Δ = b2-4ac
Δ = -162-4·1·(-161)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-30}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+30}{2*1}=\frac{46}{2}
=23
$