8=0.5x^2

Solution for 8=0.5x^2 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
$