4x^2=0.5

Solution for 4x^2=0.5 equation:

4x^2=0.5

We move all terms to the left:

4x^2-(0.5)=0

We add all the numbers together, and all the variables

4x^2-0.5=0

a = 4; b = 0; c = -0.5;
Δ = b2-4ac
Δ = 02-4·4·(-0.5)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*4}=\frac{0-2\sqrt{2}}{8}
=-\frac{2\sqrt{2}}{8}
=-\frac{\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*4}=\frac{0+2\sqrt{2}}{8}
=\frac{2\sqrt{2}}{8}
=\frac{\sqrt{2}}{4}
$