(s+6)(s-2)=228

Solution for (s+6)(s-2)=228 equation:

(s+6)(s-2)=228

We move all terms to the left:

(s+6)(s-2)-(228)=0

We multiply parentheses ..

(+s^2-2s+6s-12)-228=0

We get rid of parentheses

s^2-2s+6s-12-228=0

We add all the numbers together, and all the variables

s^2+4s-240=0

a = 1; b = 4; c = -240;
Δ = b2-4ac
Δ = 42-4·1·(-240)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{61}}{2*1}=\frac{-4-4\sqrt{61}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{61}}{2*1}=\frac{-4+4\sqrt{61}}{2}
$