Solve 6w^2=5w

$$6 w ^ { 2 } = 5 w$$

Solve for w

$$w=\frac{5}{6}\approx 0.833333333$$

$$w=0$$

Steps Using Factoring

Subtract 5w from both sides.

$$6w^{2}-5w=0$$

Factor out w.

$$w\left(6w-5\right)=0$$

To find equation solutions, solve w=0 and 6w-5=0.

$$w=0 w=\frac{5}{6}$$

Steps Using the Quadratic Formula

Subtract 5w from both sides.

$$6w^{2}-5w=0$$

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

$$w=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 6}$$

Take the square root of \left(-5\right)^{2}.

$$w=\frac{-\left(-5\right)±5}{2\times 6}$$

The opposite of -5 is 5.

$$w=\frac{5±5}{2\times 6}$$

Multiply 2 times 6.

$$w=\frac{5±5}{12}$$

Now solve the equation w=\frac{5±5}{12} when ± is plus. Add 5 to 5.

$$w=\frac{10}{12}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$w=\frac{5}{6}$$

Now solve the equation w=\frac{5±5}{12} when ± is minus. Subtract 5 from 5.

$$w=\frac{0}{12}$$

Divide 0 by 12.

$$w=0$$

The equation is now solved.

$$w=\frac{5}{6} w=0$$

Steps for Completing the Square

Subtract 5w from both sides.

$$6w^{2}-5w=0$$

Divide both sides by 6.

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

Dividing by 6 undoes the multiplication by 6.

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

Divide 0 by 6.

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

Divide -\frac{5}{6}, the coefficient of the x term, by 2 to get -\frac{5}{12}. Then add the square of -\frac{5}{12} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}-\frac{5}{6}w+\left(-\frac{5}{12}\right)^{2}=\left(-\frac{5}{12}\right)^{2}$$

Square -\frac{5}{12} by squaring both the numerator and the denominator of the fraction.

$$w^{2}-\frac{5}{6}w+\frac{25}{144}=\frac{25}{144}$$

Factor w^{2}-\frac{5}{6}w+\frac{25}{144}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(w-\frac{5}{12}\right)^{2}=\frac{25}{144}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w-\frac{5}{12}\right)^{2}}=\sqrt{\frac{25}{144}}$$

Simplify.

$$w-\frac{5}{12}=\frac{5}{12} w-\frac{5}{12}=-\frac{5}{12}$$

Add \frac{5}{12} to both sides of the equation.

$$w=\frac{5}{6} w=0$$