4215=x2

Solution for 4215=x2 equation:

4215=x2

We move all terms to the left:

4215-(x2)=0

We add all the numbers together, and all the variables

-1x^2+4215=0

a = -1; b = 0; c = +4215;
Δ = b2-4ac
Δ = 02-4·(-1)·4215
Δ = 16860
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:

$\sqrt{\Delta}=\sqrt{16860}=\sqrt{4*4215}=\sqrt{4}*\sqrt{4215}=2\sqrt{4215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4215}}{2*-1}=\frac{0-2\sqrt{4215}}{-2}
=-\frac{2\sqrt{4215}}{-2}
=-\frac{\sqrt{4215}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4215}}{2*-1}=\frac{0+2\sqrt{4215}}{-2}
=\frac{2\sqrt{4215}}{-2}
=\frac{\sqrt{4215}}{-1}
$