(x^2)-64=100

Solution for (x^2)-64=100 equation:

(x^2)-64=100

We move all terms to the left:

(x^2)-64-(100)=0

We add all the numbers together, and all the variables

x^2-164=0

a = 1; b = 0; c = -164;
Δ = b2-4ac
Δ = 02-4·1·(-164)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{41}}{2*1}=\frac{0-4\sqrt{41}}{2}
=-\frac{4\sqrt{41}}{2}
=-2\sqrt{41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{41}}{2*1}=\frac{0+4\sqrt{41}}{2}
=\frac{4\sqrt{41}}{2}
=2\sqrt{41}
$