Solve (5/6b)*b=24

$$( \frac{ 5 }{ 6 } b) \times b = 24$$

Solve for b

$$b = \frac{12 \sqrt{5}}{5} \approx 5.366563146$$

$$b = -\frac{12 \sqrt{5}}{5} \approx -5.366563146$$

Steps by Finding Square Root

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

$$\frac{5}{6}b^{2}=24$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$b^{2}=24\times \frac{6}{5}$$

Express 24\times \frac{6}{5} as a single fraction.

$$b^{2}=\frac{24\times 6}{5}$$

Multiply 24 and 6 to get 144.

$$b^{2}=\frac{144}{5}$$

Take the square root of both sides of the equation.

$$b=\frac{12\sqrt{5}}{5} b=-\frac{12\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

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

$$\frac{5}{6}b^{2}=24$$

Subtract 24 from both sides.

$$\frac{5}{6}b^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{5}{6} for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times \frac{5}{6}\left(-24\right)}}{2\times \frac{5}{6}}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times \frac{5}{6}\left(-24\right)}}{2\times \frac{5}{6}}$$

Multiply -4 times \frac{5}{6}.

$$b=\frac{0±\sqrt{-\frac{10}{3}\left(-24\right)}}{2\times \frac{5}{6}}$$

Multiply -\frac{10}{3} times -24.

$$b=\frac{0±\sqrt{80}}{2\times \frac{5}{6}}$$

Take the square root of 80.

$$b=\frac{0±4\sqrt{5}}{2\times \frac{5}{6}}$$

Multiply 2 times \frac{5}{6}.

$$b=\frac{0±4\sqrt{5}}{\frac{5}{3}}$$

Now solve the equation b=\frac{0±4\sqrt{5}}{\frac{5}{3}} when ± is plus.

$$b=\frac{12\sqrt{5}}{5}$$

Now solve the equation b=\frac{0±4\sqrt{5}}{\frac{5}{3}} when ± is minus.

$$b=-\frac{12\sqrt{5}}{5}$$

The equation is now solved.

$$b=\frac{12\sqrt{5}}{5} b=-\frac{12\sqrt{5}}{5}$$