2a^2=82

Solution for 2a^2=82 equation:

2a^2=82

We move all terms to the left:

2a^2-(82)=0

a = 2; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·2·(-82)
Δ = 656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{41}}{2*2}=\frac{0-4\sqrt{41}}{4}
=-\frac{4\sqrt{41}}{4}
=-\sqrt{41}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{41}}{2*2}=\frac{0+4\sqrt{41}}{4}
=\frac{4\sqrt{41}}{4}
=\sqrt{41}
$