2(6q2=q)-3q

Solution for 2(6q2=q)-3q equation:

2(6q^2=q)-3q

We move all terms to the left:

2(6q^2-(q)-3q)=0

We multiply parentheses

12q^2-2q-6q=0

We add all the numbers together, and all the variables

12q^2-8q=0

a = 12; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·12·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*12}=\frac{0}{24}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*12}=\frac{16}{24}
=2/3
$