Answer
$x=\displaystyle \frac{FC}{SP-VC}$
Work Step by Step
Cost $=$ Variable cost $+$ Fixed cost
$C(x)=mx+b$ is called a linear cost function
the variable cost is $mx$ and the fixed cost is $b$.
If $R(x)$ is the revenue from selling $x$ items at a price of m each, then
$R$ is the linear function $R(x)=mx$ .
Profit $=$ Revenue-Cost,$\qquad P(x)=R(x)-C(x)$
Breakeven occurs when $P=0$, or $R(x)=C(x)$.
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For the cost function,
$C(x)=VC\cdot x+FC$
The revenue: $R(x)=SP\cdot x$
Breakeven: $R(x)=C(x)$
$SP\cdot x=VC\cdot x+FC\qquad /-VC\cdot x$
$SP\cdot x-VC\cdot x=FC$
$(SP-VC)x=FC$
$x=\displaystyle \frac{FC}{SP-VC}$
