.5x^2=30

Solution for .5x^2=30 equation:

.5x^2=30

We move all terms to the left:

.5x^2-(30)=0

a = .5; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·.5·(-30)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*.5}=\frac{0-2\sqrt{15}}{1}
=-\frac{2\sqrt{15}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*.5}=\frac{0+2\sqrt{15}}{1}
=\frac{2\sqrt{15}}{1}
$