Solve for f
f=\frac{4}{\sqrt{k-7}}
k>7
Solve for k
k=7+\frac{16}{f^{2}}
f>0
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\frac{5}{4}f=\frac{5}{\sqrt{k-7}}
Swap sides so that all variable terms are on the left hand side.
\frac{\frac{5}{4}f}{\frac{5}{4}}=\frac{5}{\frac{5}{4}\sqrt{k-7}}
Divide both sides of the equation by \frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.
f=\frac{5}{\frac{5}{4}\sqrt{k-7}}
Dividing by \frac{5}{4} undoes the multiplication by \frac{5}{4}.
f=\frac{4}{\sqrt{k-7}}
Divide \frac{5}{\sqrt{k-7}} by \frac{5}{4} by multiplying \frac{5}{\sqrt{k-7}} by the reciprocal of \frac{5}{4}.
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