s+31=s2

Solution for s+31=s2 equation:

s+31=s2

We move all terms to the left:

s+31-(s2)=0

We add all the numbers together, and all the variables

-1s^2+s+31=0

a = -1; b = 1; c = +31;
Δ = b2-4ac
Δ = 12-4·(-1)·31
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{5}}{2*-1}=\frac{-1-5\sqrt{5}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{5}}{2*-1}=\frac{-1+5\sqrt{5}}{-2}
$