80-x^2=x^2-208

Solution for 80-x^2=x^2-208 equation:

80-x^2=x^2-208

We move all terms to the left:

80-x^2-(x^2-208)=0

We add all the numbers together, and all the variables

-1x^2-(x^2-208)+80=0

We get rid of parentheses

-1x^2-x^2+208+80=0

We add all the numbers together, and all the variables

-2x^2+288=0

a = -2; b = 0; c = +288;
Δ = b2-4ac
Δ = 02-4·(-2)·288
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*-2}=\frac{-48}{-4}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*-2}=\frac{48}{-4}
=-12
$