(X+4)(x-4)=500

Solution for (X+4)(x-4)=500 equation:

(X+4)(X-4)=500

We move all terms to the left:

(X+4)(X-4)-(500)=0

We use the square of the difference formula

X^2-16-500=0

We add all the numbers together, and all the variables

X^2-516=0

a = 1; b = 0; c = -516;
Δ = b2-4ac
Δ = 02-4·1·(-516)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{129}}{2*1}=\frac{0-4\sqrt{129}}{2}
=-\frac{4\sqrt{129}}{2}
=-2\sqrt{129}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{129}}{2*1}=\frac{0+4\sqrt{129}}{2}
=\frac{4\sqrt{129}}{2}
=2\sqrt{129}
$