X=-0.5x^2

Solution for X=-0.5x^2 equation:

X=-0.5X^2

We move all terms to the left:

X-(-0.5X^2)=0

We get rid of parentheses

0.5X^2+X=0

a = 0.5; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·0.5·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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