#### Answer

$3\text{ pieces}$

#### Work Step by Step

Substituting $p=7$ in the given equation, $
p=-x^2+15
,$ results to
\begin{array}{l}\require{cancel}
7=-x^2+15
\\
x^2=15-7
\\
x^2=8
.\end{array}
Taking the positive square root of both sides (since $x$ is nonnegative), the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\sqrt{8}
\\
x\approx3
.\end{array}
Hence, the demand for the desk lamp, $x,$ is $
3\text{ pieces}
.$