(q+4)(q-6)=6

Solution for (q+4)(q-6)=6 equation:

(q+4)(q-6)=6

We move all terms to the left:

(q+4)(q-6)-(6)=0

We multiply parentheses ..

(+q^2-6q+4q-24)-6=0

We get rid of parentheses

q^2-6q+4q-24-6=0

We add all the numbers together, and all the variables

q^2-2q-30=0

a = 1; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·1·(-30)
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*1}=\frac{2-2\sqrt{31}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*1}=\frac{2+2\sqrt{31}}{2}
$