Solve 7u^2=3u

$$7 u ^ { 2 } = 3 u$$

Solve for u

$$u=\frac{3}{7}\approx 0.428571429$$

$$u=0$$

Steps Using Factoring

Subtract 3u from both sides.

$$7u^{2}-3u=0$$

Factor out u.

$$u\left(7u-3\right)=0$$

To find equation solutions, solve u=0 and 7u-3=0.

$$u=0 u=\frac{3}{7}$$

Steps Using the Quadratic Formula

Subtract 3u from both sides.

$$7u^{2}-3u=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 7}$$

Take the square root of \left(-3\right)^{2}.

$$u=\frac{-\left(-3\right)±3}{2\times 7}$$

The opposite of -3 is 3.

$$u=\frac{3±3}{2\times 7}$$

Multiply 2 times 7.

$$u=\frac{3±3}{14}$$

Now solve the equation u=\frac{3±3}{14} when ± is plus. Add 3 to 3.

$$u=\frac{6}{14}$$

Reduce the fraction \frac{6}{14} to lowest terms by extracting and canceling out 2.

$$u=\frac{3}{7}$$

Now solve the equation u=\frac{3±3}{14} when ± is minus. Subtract 3 from 3.

$$u=\frac{0}{14}$$

Divide 0 by 14.

$$u=0$$

The equation is now solved.

$$u=\frac{3}{7} u=0$$

Steps for Completing the Square

Subtract 3u from both sides.

$$7u^{2}-3u=0$$

Divide both sides by 7.

$$\frac{7u^{2}-3u}{7}=\frac{0}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$u^{2}-\frac{3}{7}u=\frac{0}{7}$$

Divide 0 by 7.

$$u^{2}-\frac{3}{7}u=0$$

Divide -\frac{3}{7}, the coefficient of the x term, by 2 to get -\frac{3}{14}. Then add the square of -\frac{3}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$u^{2}-\frac{3}{7}u+\left(-\frac{3}{14}\right)^{2}=\left(-\frac{3}{14}\right)^{2}$$

Square -\frac{3}{14} by squaring both the numerator and the denominator of the fraction.

$$u^{2}-\frac{3}{7}u+\frac{9}{196}=\frac{9}{196}$$

Factor u^{2}-\frac{3}{7}u+\frac{9}{196}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(u-\frac{3}{14}\right)^{2}=\frac{9}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(u-\frac{3}{14}\right)^{2}}=\sqrt{\frac{9}{196}}$$

Simplify.

$$u-\frac{3}{14}=\frac{3}{14} u-\frac{3}{14}=-\frac{3}{14}$$

Add \frac{3}{14} to both sides of the equation.

$$u=\frac{3}{7} u=0$$