15^2+2x-8^2=x^2

Solution for 15^2+2x-8^2=x^2 equation:

15^2+2x-8^2=x^2

We move all terms to the left:

15^2+2x-8^2-(x^2)=0

determiningTheFunctionDomain
-x^2+2x+15^2-8^2=0

We add all the numbers together, and all the variables

-1x^2+2x+161=0

a = -1; b = 2; c = +161;
Δ = b2-4ac
Δ = 22-4·(-1)·161
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18\sqrt{2}}{2*-1}=\frac{-2-18\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18\sqrt{2}}{2*-1}=\frac{-2+18\sqrt{2}}{-2}
$