s(11-s)=14

Solution for s(11-s)=14 equation:

s(11-s)=14

We move all terms to the left:

s(11-s)-(14)=0

We add all the numbers together, and all the variables

s(-1s+11)-14=0

We multiply parentheses

-1s^2+11s-14=0

a = -1; b = 11; c = -14;
Δ = b2-4ac
Δ = 112-4·(-1)·(-14)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{65}}{2*-1}=\frac{-11-\sqrt{65}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{65}}{2*-1}=\frac{-11+\sqrt{65}}{-2}
$