Solve 6x^2=8x

$$6 x ^ { 2 } = 8 x$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$x=0$$

Steps Using Factoring

Subtract 8x from both sides.

$$6x^{2}-8x=0$$

Factor out x.

$$x\left(6x-8\right)=0$$

To find equation solutions, solve x=0 and 6x-8=0.

$$x=0 x=\frac{4}{3}$$

Steps Using the Quadratic Formula

Subtract 8x from both sides.

$$6x^{2}-8x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, -8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 6}$$

Take the square root of \left(-8\right)^{2}.

$$x=\frac{-\left(-8\right)±8}{2\times 6}$$

The opposite of -8 is 8.

$$x=\frac{8±8}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{8±8}{12}$$

Now solve the equation x=\frac{8±8}{12} when ± is plus. Add 8 to 8.

$$x=\frac{16}{12}$$

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{4}{3}$$

Now solve the equation x=\frac{8±8}{12} when ± is minus. Subtract 8 from 8.

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

Divide 0 by 12.

$$x=0$$

The equation is now solved.

$$x=\frac{4}{3} x=0$$

Steps for Completing the Square

Subtract 8x from both sides.

$$6x^{2}-8x=0$$

Divide both sides by 6.

$$\frac{6x^{2}-8x}{6}=\frac{0}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x^{2}+\left(-\frac{8}{6}\right)x=\frac{0}{6}$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{4}{3}x=\frac{0}{6}$$

Divide 0 by 6.

$$x^{2}-\frac{4}{3}x=0$$

Divide -\frac{4}{3}, the coefficient of the x term, by 2 to get -\frac{2}{3}. Then add the square of -\frac{2}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{4}{3}x+\left(-\frac{2}{3}\right)^{2}=\left(-\frac{2}{3}\right)^{2}$$

Square -\frac{2}{3} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{4}{9}$$

Factor x^{2}-\frac{4}{3}x+\frac{4}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{2}{3}\right)^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{2}{3}\right)^{2}}=\sqrt{\frac{4}{9}}$$

Simplify.

$$x-\frac{2}{3}=\frac{2}{3} x-\frac{2}{3}=-\frac{2}{3}$$

Add \frac{2}{3} to both sides of the equation.

$$x=\frac{4}{3} x=0$$