(q+8)(q+6)=3

Solution for (q+8)(q+6)=3 equation:

(q+8)(q+6)=3

We move all terms to the left:

(q+8)(q+6)-(3)=0

We multiply parentheses ..

(+q^2+6q+8q+48)-3=0

We get rid of parentheses

q^2+6q+8q+48-3=0

We add all the numbers together, and all the variables

q^2+14q+45=0

a = 1; b = 14; c = +45;
Δ = b2-4ac
Δ = 142-4·1·45
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4}{2*1}=\frac{-18}{2}
=-9
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*1}=\frac{-10}{2}
=-5
$