s+81=s2

Solution for s+81=s2 equation:

s+81=s2

We move all terms to the left:

s+81-(s2)=0

We add all the numbers together, and all the variables

-1s^2+s+81=0

a = -1; b = 1; c = +81;
Δ = b2-4ac
Δ = 12-4·(-1)·81
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{13}}{2*-1}=\frac{-1-5\sqrt{13}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{13}}{2*-1}=\frac{-1+5\sqrt{13}}{-2}
$