120=0.5c2

Solution for 120=0.5c2 equation:

120=0.5c^2

We move all terms to the left:

120-(0.5c^2)=0

We get rid of parentheses

-0.5c^2+120=0

a = -0.5; b = 0; c = +120;
Δ = b2-4ac
Δ = 02-4·(-0.5)·120
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-0.5}=\frac{0-4\sqrt{15}}{-1}
=-\frac{4\sqrt{15}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-0.5}=\frac{0+4\sqrt{15}}{-1}
=\frac{4\sqrt{15}}{-1}
$