18=0.5*x^2

Solution for 18=0.5*x^2 equation:

18=0.5x^2

We move all terms to the left:

18-(0.5x^2)=0

We get rid of parentheses

-0.5x^2+18=0

a = -0.5; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-0.5)·18
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*-0.5}=\frac{-6}{-1}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-0.5}=\frac{6}{-1}
=-6
$