2(2q-3)(q-1)=0

Solution for 2(2q-3)(q-1)=0 equation:

2(2q-3)(q-1)=0

We multiply parentheses ..

2(+2q^2-2q-3q+3)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

4q^2-10q+6=0

a = 4; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·4·6
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*4}=\frac{8}{8}
=1
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*4}=\frac{12}{8}
=1+1/2
$