2(x^2-6)=82

Solution for 2(x^2-6)=82 equation:

2(x^2-6)=82

We move all terms to the left:

2(x^2-6)-(82)=0

We multiply parentheses

2x^2-12-82=0

We add all the numbers together, and all the variables

2x^2-94=0

a = 2; b = 0; c = -94;
Δ = b2-4ac
Δ = 02-4·2·(-94)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{47}}{2*2}=\frac{0-4\sqrt{47}}{4}
=-\frac{4\sqrt{47}}{4}
=-\sqrt{47}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{47}}{2*2}=\frac{0+4\sqrt{47}}{4}
=\frac{4\sqrt{47}}{4}
=\sqrt{47}
$