4213=y2+14

Solution for 4213=y2+14 equation:

4213=y2+14

We move all terms to the left:

4213-(y2+14)=0

We add all the numbers together, and all the variables

-(+y^2+14)+4213=0

We get rid of parentheses

-y^2-14+4213=0

We add all the numbers together, and all the variables

-1y^2+4199=0

a = -1; b = 0; c = +4199;
Δ = b2-4ac
Δ = 02-4·(-1)·4199
Δ = 16796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16796}=\sqrt{4*4199}=\sqrt{4}*\sqrt{4199}=2\sqrt{4199}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4199}}{2*-1}=\frac{0-2\sqrt{4199}}{-2}
=-\frac{2\sqrt{4199}}{-2}
=-\frac{\sqrt{4199}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4199}}{2*-1}=\frac{0+2\sqrt{4199}}{-2}
=\frac{2\sqrt{4199}}{-2}
=\frac{\sqrt{4199}}{-1}
$