x^2=415

Solution for x^2=415 equation:

x^2=415

We move all terms to the left:

x^2-(415)=0

a = 1; b = 0; c = -415;
Δ = b2-4ac
Δ = 02-4·1·(-415)
Δ = 1660
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:

$\sqrt{\Delta}=\sqrt{1660}=\sqrt{4*415}=\sqrt{4}*\sqrt{415}=2\sqrt{415}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{415}}{2*1}=\frac{0-2\sqrt{415}}{2}
=-\frac{2\sqrt{415}}{2}
=-\sqrt{415}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{415}}{2*1}=\frac{0+2\sqrt{415}}{2}
=\frac{2\sqrt{415}}{2}
=\sqrt{415}
$