(x-4)2=x2-40

Solution for (x-4)2=x2-40 equation:

(x-4)2=x2-40

We move all terms to the left:

(x-4)2-(x2-40)=0

We add all the numbers together, and all the variables

-(+x^2-40)+(x-4)2=0

We multiply parentheses

-(+x^2-40)+2x-8=0

We get rid of parentheses

-x^2+2x+40-8=0

We add all the numbers together, and all the variables

-1x^2+2x+32=0

a = -1; b = 2; c = +32;
Δ = b2-4ac
Δ = 22-4·(-1)·32
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*-1}=\frac{-2-2\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*-1}=\frac{-2+2\sqrt{33}}{-2}
$