x^2=416

Solution for x^2=416 equation:

x^2=416

We move all terms to the left:

x^2-(416)=0

a = 1; b = 0; c = -416;
Δ = b2-4ac
Δ = 02-4·1·(-416)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{26}}{2*1}=\frac{0-8\sqrt{26}}{2}
=-\frac{8\sqrt{26}}{2}
=-4\sqrt{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{26}}{2*1}=\frac{0+8\sqrt{26}}{2}
=\frac{8\sqrt{26}}{2}
=4\sqrt{26}
$