x^2+4=221

Solution for x^2+4=221 equation:

x^2+4=221

We move all terms to the left:

x^2+4-(221)=0

We add all the numbers together, and all the variables

x^2-217=0

a = 1; b = 0; c = -217;
Δ = b2-4ac
Δ = 02-4·1·(-217)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{217}}{2*1}=\frac{0-2\sqrt{217}}{2}
=-\frac{2\sqrt{217}}{2}
=-\sqrt{217}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{217}}{2*1}=\frac{0+2\sqrt{217}}{2}
=\frac{2\sqrt{217}}{2}
=\sqrt{217}
$