12*x^2=0,5

Solution for 12*x^2=0,5 equation:

12x^2=0.5

We move all terms to the left:

12x^2-(0.5)=0

We add all the numbers together, and all the variables

12x^2-0.5=0

a = 12; b = 0; c = -0.5;
Δ = b2-4ac
Δ = 02-4·12·(-0.5)
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*12}=\frac{0-2\sqrt{6}}{24}
=-\frac{2\sqrt{6}}{24}
=-\frac{\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*12}=\frac{0+2\sqrt{6}}{24}
=\frac{2\sqrt{6}}{24}
=\frac{\sqrt{6}}{12}
$