15=x^2-16

Solution for 15=x^2-16 equation:

15=x^2-16

We move all terms to the left:

15-(x^2-16)=0

We get rid of parentheses

-x^2+16+15=0

We add all the numbers together, and all the variables

-1x^2+31=0

a = -1; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-1)·31
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{31}}{2*-1}=\frac{0-2\sqrt{31}}{-2}
=-\frac{2\sqrt{31}}{-2}
=-\frac{\sqrt{31}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{31}}{2*-1}=\frac{0+2\sqrt{31}}{-2}
=\frac{2\sqrt{31}}{-2}
=\frac{\sqrt{31}}{-1}
$