(q-1)(q-6)=-6

Solution for (q-1)(q-6)=-6 equation:

(q-1)(q-6)=-6

We move all terms to the left:

(q-1)(q-6)-(-6)=0

We add all the numbers together, and all the variables

(q-1)(q-6)+6=0

We multiply parentheses ..

(+q^2-6q-1q+6)+6=0

We get rid of parentheses

q^2-6q-1q+6+6=0

We add all the numbers together, and all the variables

q^2-7q+12=0

a = 1; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·1·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*1}=\frac{6}{2}
=3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*1}=\frac{8}{2}
=4
$