X+16=y^2

Solution for X+16=y^2 equation:

X+16=X^2

We move all terms to the left:

X+16-(X^2)=0

determiningTheFunctionDomain
-X^2+X+16=0

We add all the numbers together, and all the variables

-1X^2+X+16=0

a = -1; b = 1; c = +16;
Δ = b2-4ac
Δ = 12-4·(-1)·16
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{65}}{2*-1}=\frac{-1-\sqrt{65}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*-1}=\frac{-1+\sqrt{65}}{-2}
$