Solve TC=(sqrt[r]{e/gamma-1})*100

$$T C = ( \sqrt[ r ] { \frac { e } { \gamma } - 1 } ) \times 100$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{T}\text{, }&T\neq 0\text{ and }\gamma \neq 0\text{ and }r\neq 0\\C\in \mathrm{C}\text{, }&r\neq 0\text{ and }T=0\text{ and }\gamma =e\end{matrix}\right.$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\gamma }{\gamma }.

$$TC=\sqrt[r]{\frac{e}{\gamma }-\frac{\gamma }{\gamma }}\times 100$$

Since \frac{e}{\gamma } and \frac{\gamma }{\gamma } have the same denominator, subtract them by subtracting their numerators.

$$TC=\sqrt[r]{\frac{e-\gamma }{\gamma }}\times 100$$

The equation is in standard form.

$$TC=100\sqrt[r]{\frac{e-\gamma }{\gamma }}$$

Divide both sides by T.

$$\frac{TC}{T}=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{T}$$

Dividing by T undoes the multiplication by T.

$$C=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{T}$$

Solve for T (complex solution)

$$\left\{\begin{matrix}T=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{C}\text{, }&C\neq 0\text{ and }\gamma \neq 0\text{ and }r\neq 0\\T\in \mathrm{C}\text{, }&r\neq 0\text{ and }C=0\text{ and }\gamma =e\end{matrix}\right.$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\gamma }{\gamma }.

$$TC=\sqrt[r]{\frac{e}{\gamma }-\frac{\gamma }{\gamma }}\times 100$$

Since \frac{e}{\gamma } and \frac{\gamma }{\gamma } have the same denominator, subtract them by subtracting their numerators.

$$TC=\sqrt[r]{\frac{e-\gamma }{\gamma }}\times 100$$

The equation is in standard form.

$$CT=100\sqrt[r]{\frac{e-\gamma }{\gamma }}$$

Divide both sides by C.

$$\frac{CT}{C}=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{C}$$

Dividing by C undoes the multiplication by C.

$$T=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{C}$$

Solve for C

$$\left\{\begin{matrix}C=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{T}\text{, }&\left(T\neq 0\text{ and }\gamma <e\text{ and }\gamma >0\text{ and }r\neq 0\right)\text{ or }\left(T\neq 0\text{ and }\gamma =e\text{ and }r>0\right)\text{ or }\left(T\neq 0\text{ and }Numerator(r)\text{bmod}2=1\text{ and }\gamma <0\text{ and }Denominator(r)\text{bmod}2=1\right)\text{ or }\left(T\neq 0\text{ and }Numerator(r)\text{bmod}2=1\text{ and }\gamma >e\text{ and }Denominator(r)\text{bmod}2=1\right)\\C\in \mathrm{R}\text{, }&\gamma =e\text{ and }r>0\text{ and }T=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\gamma }{\gamma }.

$$TC=\sqrt[r]{\frac{e}{\gamma }-\frac{\gamma }{\gamma }}\times 100$$

Since \frac{e}{\gamma } and \frac{\gamma }{\gamma } have the same denominator, subtract them by subtracting their numerators.

$$TC=\sqrt[r]{\frac{e-\gamma }{\gamma }}\times 100$$

The equation is in standard form.

$$TC=100\sqrt[r]{\frac{e-\gamma }{\gamma }}$$

Divide both sides by T.

$$\frac{TC}{T}=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{T}$$

Dividing by T undoes the multiplication by T.

$$C=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{T}$$

Solve for T

$$\left\{\begin{matrix}T=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{C}\text{, }&\left(C\neq 0\text{ and }\gamma <e\text{ and }\gamma >0\text{ and }r\neq 0\right)\text{ or }\left(C\neq 0\text{ and }\gamma =e\text{ and }r>0\right)\text{ or }\left(C\neq 0\text{ and }Numerator(r)\text{bmod}2=1\text{ and }\gamma <0\text{ and }Denominator(r)\text{bmod}2=1\right)\text{ or }\left(C\neq 0\text{ and }Numerator(r)\text{bmod}2=1\text{ and }\gamma >e\text{ and }Denominator(r)\text{bmod}2=1\right)\\T\in \mathrm{R}\text{, }&\gamma =e\text{ and }r>0\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\gamma }{\gamma }.

$$TC=\sqrt[r]{\frac{e}{\gamma }-\frac{\gamma }{\gamma }}\times 100$$

Since \frac{e}{\gamma } and \frac{\gamma }{\gamma } have the same denominator, subtract them by subtracting their numerators.

$$TC=\sqrt[r]{\frac{e-\gamma }{\gamma }}\times 100$$

The equation is in standard form.

$$CT=100\sqrt[r]{\frac{e-\gamma }{\gamma }}$$

Divide both sides by C.

$$\frac{CT}{C}=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{C}$$

Dividing by C undoes the multiplication by C.

$$T=\frac{100\left(-1+\frac{e}{\gamma }\right)^{\frac{1}{r}}}{C}$$