Answer:
[tex]q=2[/tex]
Step-by-step explanation:
We need to find the quantity demanded if the price of the shed is 1480$. Hence:
[tex]D(q)=1480=-4q^{2}-2q+1500[/tex]
Sustract 1480 to both sides:
[tex]-4q^{2} -2q+20=0[/tex]
Multiply both sides by [tex]\frac{-1}{4}[/tex]
[tex]q^{2}+\frac{1}{2}q-5=0[/tex]
We have a quadratic equation, we can solve it using the cuadratic formula or simply factoring it:
[tex](q+\frac{5}{2})(q-2)[/tex]
Now the solutions are given by:
[tex]q_1=-\frac{5}{2} \\q_2=2[/tex]
Since we look for a coherent answer we take the positive solution [tex]q_2[/tex]
So the quantity demanded is [tex]q=2[/tex]
