(x-4)=x^2-8x-16

Solution for (x-4)=x^2-8x-16 equation:

(x-4)=x^2-8x-16

We move all terms to the left:

(x-4)-(x^2-8x-16)=0

We get rid of parentheses

-x^2+x+8x-4+16=0

We add all the numbers together, and all the variables

-1x^2+9x+12=0

a = -1; b = 9; c = +12;
Δ = b2-4ac
Δ = 92-4·(-1)·12
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{129}}{2*-1}=\frac{-9-\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*-1}=\frac{-9+\sqrt{129}}{-2}
$