(x-4)(x-4)-16=240

Solution for (x-4)(x-4)-16=240 equation:

(x-4)(x-4)-16=240

We move all terms to the left:

(x-4)(x-4)-16-(240)=0

We add all the numbers together, and all the variables

(x-4)(x-4)-256=0

We multiply parentheses ..

(+x^2-4x-4x+16)-256=0

We get rid of parentheses

x^2-4x-4x+16-256=0

We add all the numbers together, and all the variables

x^2-8x-240=0

a = 1; b = -8; c = -240;
Δ = b2-4ac
Δ = -82-4·1·(-240)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-32}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+32}{2*1}=\frac{40}{2}
=20
$