x^2=421

Solution for x^2=421 equation:

x^2=421

We move all terms to the left:

x^2-(421)=0

a = 1; b = 0; c = -421;
Δ = b2-4ac
Δ = 02-4·1·(-421)
Δ = 1684
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:

$\sqrt{\Delta}=\sqrt{1684}=\sqrt{4*421}=\sqrt{4}*\sqrt{421}=2\sqrt{421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{421}}{2*1}=\frac{0-2\sqrt{421}}{2}
=-\frac{2\sqrt{421}}{2}
=-\sqrt{421}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{421}}{2*1}=\frac{0+2\sqrt{421}}{2}
=\frac{2\sqrt{421}}{2}
=\sqrt{421}
$