s^2-16=81

Solution for s^2-16=81 equation:

s^2-16=81

We move all terms to the left:

s^2-16-(81)=0

We add all the numbers together, and all the variables

s^2-97=0

a = 1; b = 0; c = -97;
Δ = b2-4ac
Δ = 02-4·1·(-97)
Δ = 388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{97}}{2*1}=\frac{0-2\sqrt{97}}{2}
=-\frac{2\sqrt{97}}{2}
=-\sqrt{97}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{97}}{2*1}=\frac{0+2\sqrt{97}}{2}
=\frac{2\sqrt{97}}{2}
=\sqrt{97}
$