300-6q-q^2=D(q)

Solution for 300-6q-q^2=D(q) equation:

300-6q-q^2=(q)

We move all terms to the left:

300-6q-q^2-((q))=0

determiningTheFunctionDomain
-q^2-6q-q+300=0

We add all the numbers together, and all the variables

-1q^2-7q+300=0

a = -1; b = -7; c = +300;
Δ = b2-4ac
Δ = -72-4·(-1)·300
Δ = 1249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1249}}{2*-1}=\frac{7-\sqrt{1249}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1249}}{2*-1}=\frac{7+\sqrt{1249}}{-2}
$