(x^2-16^2)=16x+1

Solution for (x^2-16^2)=16x+1 equation:

(x^2-16^2)=16x+1

We move all terms to the left:

(x^2-16^2)-(16x+1)=0

We get rid of parentheses

x^2-16x-1-16^2=0

We add all the numbers together, and all the variables

x^2-16x-257=0

a = 1; b = -16; c = -257;
Δ = b2-4ac
Δ = -162-4·1·(-257)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{321}}{2*1}=\frac{16-2\sqrt{321}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{321}}{2*1}=\frac{16+2\sqrt{321}}{2}
$