2a^2=2116

Solution for 2a^2=2116 equation:

2a^2=2116

We move all terms to the left:

2a^2-(2116)=0

a = 2; b = 0; c = -2116;
Δ = b2-4ac
Δ = 02-4·2·(-2116)
Δ = 16928
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:

$\sqrt{\Delta}=\sqrt{16928}=\sqrt{8464*2}=\sqrt{8464}*\sqrt{2}=92\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-92\sqrt{2}}{2*2}=\frac{0-92\sqrt{2}}{4}
=-\frac{92\sqrt{2}}{4}
=-23\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+92\sqrt{2}}{2*2}=\frac{0+92\sqrt{2}}{4}
=\frac{92\sqrt{2}}{4}
=23\sqrt{2}
$