2x^2=361

Solution for 2x^2=361 equation:

2x^2=361

We move all terms to the left:

2x^2-(361)=0

a = 2; b = 0; c = -361;
Δ = b2-4ac
Δ = 02-4·2·(-361)
Δ = 2888
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:

$\sqrt{\Delta}=\sqrt{2888}=\sqrt{1444*2}=\sqrt{1444}*\sqrt{2}=38\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38\sqrt{2}}{2*2}=\frac{0-38\sqrt{2}}{4}
=-\frac{38\sqrt{2}}{4}
=-\frac{19\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38\sqrt{2}}{2*2}=\frac{0+38\sqrt{2}}{4}
=\frac{38\sqrt{2}}{4}
=\frac{19\sqrt{2}}{2}
$