-q-1/3q=12

Solution for -q-1/3q=12 equation:

-q-1/3q=12

We move all terms to the left:

-q-1/3q-(12)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R


We add all the numbers together, and all the variables

-1q-1/3q-12=0

We multiply all the terms by the denominator


-1q*3q-12*3q-1=0

Wy multiply elements

-3q^2-36q-1=0

a = -3; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·(-3)·(-1)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{321}}{2*-3}=\frac{36-2\sqrt{321}}{-6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{321}}{2*-3}=\frac{36+2\sqrt{321}}{-6}
$