Solve for C
C=\frac{x}{4}+\alpha +\frac{1}{x}
x\neq 0
Solve for x
x=2\left(-\sqrt{\left(C-\alpha \right)^{2}-1}+C-\alpha \right)
x=2\left(\sqrt{\left(C-\alpha \right)^{2}-1}+C-\alpha \right)\text{, }C\leq \alpha -1\text{ or }C\geq \alpha +1
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xC=x\alpha +\frac{x^{2}}{4}+1
The equation is in standard form.
\frac{xC}{x}=\frac{x\alpha +\frac{x^{2}}{4}+1}{x}
Divide both sides by x.
C=\frac{x\alpha +\frac{x^{2}}{4}+1}{x}
Dividing by x undoes the multiplication by x.
C=\frac{x}{4}+\alpha +\frac{1}{x}
Divide 1+\alpha x+\frac{x^{2}}{4} by x.
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