4x^2-2=106

Solution for 4x^2-2=106 equation:

4x^2-2=106

We move all terms to the left:

4x^2-2-(106)=0

We add all the numbers together, and all the variables

4x^2-108=0

a = 4; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·4·(-108)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*4}=\frac{0-24\sqrt{3}}{8}
=-\frac{24\sqrt{3}}{8}
=-3\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*4}=\frac{0+24\sqrt{3}}{8}
=\frac{24\sqrt{3}}{8}
=3\sqrt{3}
$