x^2=456

Solution for x^2=456 equation:

x^2=456

We move all terms to the left:

x^2-(456)=0

a = 1; b = 0; c = -456;
Δ = b2-4ac
Δ = 02-4·1·(-456)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{114}}{2*1}=\frac{0-4\sqrt{114}}{2}
=-\frac{4\sqrt{114}}{2}
=-2\sqrt{114}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{114}}{2*1}=\frac{0+4\sqrt{114}}{2}
=\frac{4\sqrt{114}}{2}
=2\sqrt{114}
$