-0,5*(3*x^2-12)=0

Solution for -0,5*(3*x^2-12)=0 equation:

-0.5(3x^2-12)=0

We multiply parentheses

-1.5x^2+6=0

a = -1.5; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-1.5)·6
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-1.5}=\frac{-6}{-3}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-1.5}=\frac{6}{-3}
=-2
$