Solve for b u = square root of Gb-R

$u = \sqrt{G b - R}$

Rewrite the equation as $\sqrt{G b - R} = u$ .

$\sqrt{G b - R} = u$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{G b - R}}^{2} = u^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{G b - R}$ as ${(G b - R)}^{\frac{1}{2}}$ .

${({(G b - R)}^{\frac{1}{2}})}^{2} = u^{2}$

Simplify the left side.

Simplify ${({(G b - R)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(G b - R)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(G b - R)}^{\frac{1}{2} \cdot 2} = u^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(G b - R)}^{\frac{1}{2} \cdot 2} = u^{2}$

Rewrite the expression.

${(G b - R)}^{1} = u^{2}$

Simplify.

$G b - R = u^{2}$

Solve for $b$ .

Add $R$ to both sides of the equation.

$G b = u^{2} + R$

Divide each term in $G b = u^{2} + R$ by $G$ and simplify.

Divide each term in $G b = u^{2} + R$ by $G$ .

$\frac{G b}{G} = \frac{u^{2}}{G} + \frac{R}{G}$

Simplify the left side.

Cancel the common factor of $G$ .

Cancel the common factor.

$\frac{G b}{G} = \frac{u^{2}}{G} + \frac{R}{G}$

Divide $b$ by $1$ .

$b = \frac{u^{2}}{G} + \frac{R}{G}$