0.5x2=12

Solution for 0.5x2=12 equation:

0.5x^2=12

We move all terms to the left:

0.5x^2-(12)=0

a = 0.5; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·0.5·(-12)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*0.5}=\frac{0-2\sqrt{6}}{1}
=-\frac{2\sqrt{6}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*0.5}=\frac{0+2\sqrt{6}}{1}
=\frac{2\sqrt{6}}{1}
$