Solve u^2/3=34/6/2-3{left(frac{5/6right)}^2}{5}

$$\frac{ { u }^{ 2 } }{ 3 } = \frac{ 3 \frac{ 4 }{ 6 } }{ 2 } - \frac{ 3 { \left( \frac{ 5 }{ 6 } \right) }^{ 2 } }{ 5 }$$

Solve for u

$$u = \frac{\sqrt{17}}{2} \approx 2.061552813$$

$$u = -\frac{\sqrt{17}}{2} \approx -2.061552813$$

Steps by Finding Square Root

Multiply both sides of the equation by 30, the least common multiple of 3,2,5.

$$10u^{2}=15\times \frac{3\times 6+4}{6}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Multiply 3 and 6 to get 18.

$$10u^{2}=15\times \frac{18+4}{6}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Add 18 and 4 to get 22.

$$10u^{2}=15\times \frac{22}{6}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$10u^{2}=15\times \frac{11}{3}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Multiply 15 and \frac{11}{3} to get 55.

$$10u^{2}=55-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Multiply -6 and 3 to get -18.

$$10u^{2}=55-18\times \left(\frac{5}{6}\right)^{2}$$

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$10u^{2}=55-18\times \frac{25}{36}$$

Multiply -18 and \frac{25}{36} to get -\frac{25}{2}.

$$10u^{2}=55-\frac{25}{2}$$

Subtract \frac{25}{2} from 55 to get \frac{85}{2}.

$$10u^{2}=\frac{85}{2}$$

Divide both sides by 10.

$$u^{2}=\frac{\frac{85}{2}}{10}$$

Express \frac{\frac{85}{2}}{10} as a single fraction.

$$u^{2}=\frac{85}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$u^{2}=\frac{85}{20}$$

Reduce the fraction \frac{85}{20} to lowest terms by extracting and canceling out 5.

$$u^{2}=\frac{17}{4}$$

Take the square root of both sides of the equation.

$$u=\frac{\sqrt{17}}{2} u=-\frac{\sqrt{17}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 30, the least common multiple of 3,2,5.

$$10u^{2}=15\times \frac{3\times 6+4}{6}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Multiply 3 and 6 to get 18.

$$10u^{2}=15\times \frac{18+4}{6}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Add 18 and 4 to get 22.

$$10u^{2}=15\times \frac{22}{6}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$10u^{2}=15\times \frac{11}{3}-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Multiply 15 and \frac{11}{3} to get 55.

$$10u^{2}=55-6\times 3\times \left(\frac{5}{6}\right)^{2}$$

Multiply -6 and 3 to get -18.

$$10u^{2}=55-18\times \left(\frac{5}{6}\right)^{2}$$

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$10u^{2}=55-18\times \frac{25}{36}$$

Multiply -18 and \frac{25}{36} to get -\frac{25}{2}.

$$10u^{2}=55-\frac{25}{2}$$

Subtract \frac{25}{2} from 55 to get \frac{85}{2}.

$$10u^{2}=\frac{85}{2}$$

Subtract \frac{85}{2} from both sides.

$$10u^{2}-\frac{85}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -\frac{85}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{0±\sqrt{0^{2}-4\times 10\left(-\frac{85}{2}\right)}}{2\times 10}$$

Square 0.

$$u=\frac{0±\sqrt{-4\times 10\left(-\frac{85}{2}\right)}}{2\times 10}$$

Multiply -4 times 10.

$$u=\frac{0±\sqrt{-40\left(-\frac{85}{2}\right)}}{2\times 10}$$

Multiply -40 times -\frac{85}{2}.

$$u=\frac{0±\sqrt{1700}}{2\times 10}$$

Take the square root of 1700.

$$u=\frac{0±10\sqrt{17}}{2\times 10}$$

Multiply 2 times 10.

$$u=\frac{0±10\sqrt{17}}{20}$$

Now solve the equation u=\frac{0±10\sqrt{17}}{20} when ± is plus.

$$u=\frac{\sqrt{17}}{2}$$

Now solve the equation u=\frac{0±10\sqrt{17}}{20} when ± is minus.

$$u=-\frac{\sqrt{17}}{2}$$

The equation is now solved.

$$u=\frac{\sqrt{17}}{2} u=-\frac{\sqrt{17}}{2}$$