.5x^2=6

Solution for .5x^2=6 equation:

.5x^2=6

We move all terms to the left:

.5x^2-(6)=0

a = .5; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·.5·(-6)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*.5}=\frac{0-2\sqrt{3}}{1}
=-\frac{2\sqrt{3}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*.5}=\frac{0+2\sqrt{3}}{1}
=\frac{2\sqrt{3}}{1}
$