s(s-49)=s+31

Solution for s(s-49)=s+31 equation:

s(s-49)=s+31

We move all terms to the left:

s(s-49)-(s+31)=0

We multiply parentheses

s^2-49s-(s+31)=0

We get rid of parentheses

s^2-49s-s-31=0

We add all the numbers together, and all the variables

s^2-50s-31=0

a = 1; b = -50; c = -31;
Δ = b2-4ac
Δ = -502-4·1·(-31)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-8\sqrt{41}}{2*1}=\frac{50-8\sqrt{41}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+8\sqrt{41}}{2*1}=\frac{50+8\sqrt{41}}{2}
$