-8=-0.5x2

Solution for -8=-0.5x2 equation:

-8=-0.5x^2

We move all terms to the left:

-8-(-0.5x^2)=0

We get rid of parentheses

0.5x^2-8=0

a = 0.5; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·0.5·(-8)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*0.5}=\frac{-4}{1}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*0.5}=\frac{4}{1}
=4
$