Solve (1+M(RR)=sqrt[6]{2*463}

$$( 1 + M ( R R ) = \sqrt[ 6 ] { 2 \cdot 463 }$$

Solve for M

$$M=\frac{\sqrt[6]{926}-1}{R^{2}}$$

$$R\neq 0$$

Steps for Solving Linear Equation

Multiply R and R to get R^{2}.

$$1+MR^{2}=\sqrt[6]{2\times 463}$$

Multiply 2 and 463 to get 926.

$$1+MR^{2}=\sqrt[6]{926}$$

Subtract 1 from both sides.

$$MR^{2}=\sqrt[6]{926}-1$$

The equation is in standard form.

$$R^{2}M=\sqrt[6]{926}-1$$

Divide both sides by R^{2}.

$$\frac{R^{2}M}{R^{2}}=\frac{\sqrt[6]{926}-1}{R^{2}}$$

Dividing by R^{2} undoes the multiplication by R^{2}.

$$M=\frac{\sqrt[6]{926}-1}{R^{2}}$$

Solve for R (complex solution)

$$R=-\sqrt{\sqrt[6]{926}-1}M^{-\frac{1}{2}}$$

$$R=\sqrt{\sqrt[6]{926}-1}M^{-\frac{1}{2}}\text{, }M\neq 0$$

Solve for R

$$R=\sqrt{\frac{\sqrt[6]{926}-1}{M}}$$

$$R=-\sqrt{\frac{\sqrt[6]{926}-1}{M}}\text{, }M>0$$