(s-3)(s-8)=-4

Solution for (s-3)(s-8)=-4 equation:

(s-3)(s-8)=-4

We move all terms to the left:

(s-3)(s-8)-(-4)=0

We add all the numbers together, and all the variables

(s-3)(s-8)+4=0

We multiply parentheses ..

(+s^2-8s-3s+24)+4=0

We get rid of parentheses

s^2-8s-3s+24+4=0

We add all the numbers together, and all the variables

s^2-11s+28=0

a = 1; b = -11; c = +28;
Δ = b2-4ac
Δ = -112-4·1·28
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*1}=\frac{8}{2}
=4
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*1}=\frac{14}{2}
=7
$