(4(119))^2=2a^2

Solution for (4(119))^2=2a^2 equation:

(4(119))^2=2a^2

We move all terms to the left:

(4(119))^2-(2a^2)=0

determiningTheFunctionDomain
-2a^2+4119^2=0

We add all the numbers together, and all the variables

-2a^2+16966161=0

a = -2; b = 0; c = +16966161;
Δ = b2-4ac
Δ = 02-4·(-2)·16966161
Δ = 135729288
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:

$\sqrt{\Delta}=\sqrt{135729288}=\sqrt{67864644*2}=\sqrt{67864644}*\sqrt{2}=8238\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8238\sqrt{2}}{2*-2}=\frac{0-8238\sqrt{2}}{-4}
=-\frac{8238\sqrt{2}}{-4}
=-\frac{4119\sqrt{2}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8238\sqrt{2}}{2*-2}=\frac{0+8238\sqrt{2}}{-4}
=\frac{8238\sqrt{2}}{-4}
=\frac{4119\sqrt{2}}{-2}
$