7=12-12q+3q^2

Solution for 7=12-12q+3q^2 equation:

7=12-12q+3q^2

We move all terms to the left:

7-(12-12q+3q^2)=0

We get rid of parentheses

-3q^2+12q-12+7=0

We add all the numbers together, and all the variables

-3q^2+12q-5=0

a = -3; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·(-3)·(-5)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{21}}{2*-3}=\frac{-12-2\sqrt{21}}{-6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{21}}{2*-3}=\frac{-12+2\sqrt{21}}{-6}
$