Solve R^2=1/3+(7/3-R)^2

$$R ^ { 2 } = \frac { 1 } { 3 } + ( \frac { 7 } { 3 } - R ) ^ { 2 }$$

Solve for R

$$R = \frac{26}{21} = 1\frac{5}{21} \approx 1.238095238$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{7}{3}-R\right)^{2}.

$$R^{2}=\frac{1}{3}+\frac{49}{9}-\frac{14}{3}R+R^{2}$$

Add \frac{1}{3} and \frac{49}{9} to get \frac{52}{9}.

$$R^{2}=\frac{52}{9}-\frac{14}{3}R+R^{2}$$

Add \frac{14}{3}R to both sides.

$$R^{2}+\frac{14}{3}R=\frac{52}{9}+R^{2}$$

Subtract R^{2} from both sides.

$$R^{2}+\frac{14}{3}R-R^{2}=\frac{52}{9}$$

Combine R^{2} and -R^{2} to get 0.

$$\frac{14}{3}R=\frac{52}{9}$$

Multiply both sides by \frac{3}{14}, the reciprocal of \frac{14}{3}.

$$R=\frac{52}{9}\times \frac{3}{14}$$

Multiply \frac{52}{9} and \frac{3}{14} to get \frac{26}{21}.

$$R=\frac{26}{21}$$