2*x^2=41^2

Solution for 2*x^2=41^2 equation:

2x^2=41^2

We move all terms to the left:

2x^2-(41^2)=0

We add all the numbers together, and all the variables

2x^2-1681=0

a = 2; b = 0; c = -1681;
Δ = b2-4ac
Δ = 02-4·2·(-1681)
Δ = 13448
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:

$\sqrt{\Delta}=\sqrt{13448}=\sqrt{6724*2}=\sqrt{6724}*\sqrt{2}=82\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-82\sqrt{2}}{2*2}=\frac{0-82\sqrt{2}}{4}
=-\frac{82\sqrt{2}}{4}
=-\frac{41\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+82\sqrt{2}}{2*2}=\frac{0+82\sqrt{2}}{4}
=\frac{82\sqrt{2}}{4}
=\frac{41\sqrt{2}}{2}
$