0.5x^2=x^2-2

Solution for 0.5x^2=x^2-2 equation:

0.5x^2=x^2-2

We move all terms to the left:

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

We get rid of parentheses

0.5x^2-x^2+2=0

We add all the numbers together, and all the variables

-0.5x^2+2=0

a = -0.5; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-0.5)·2
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*-0.5}=\frac{-2}{-1}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*-0.5}=\frac{2}{-1}
=-2
$