0.5x^2+32^2=x^2

Solution for 0.5x^2+32^2=x^2 equation:

0.5x^2+32^2=x^2

We move all terms to the left:

0.5x^2+32^2-(x^2)=0

We add all the numbers together, and all the variables

-0.5x^2+1024=0

a = -0.5; b = 0; c = +1024;
Δ = b2-4ac
Δ = 02-4·(-0.5)·1024
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{2}}{2*-0.5}=\frac{0-32\sqrt{2}}{-1}
=-\frac{32\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*-0.5}=\frac{0+32\sqrt{2}}{-1}
=\frac{32\sqrt{2}}{-1}
$