Solve 12x^2=7x

$$12 x ^ { 2 } = 7 x$$

Solve for x

$$x=\frac{7}{12}\approx 0.583333333$$

$$x=0$$

Steps Using Factoring

Subtract 7x from both sides.

$$12x^{2}-7x=0$$

Factor out x.

$$x\left(12x-7\right)=0$$

To find equation solutions, solve x=0 and 12x-7=0.

$$x=0 x=\frac{7}{12}$$

Steps Using the Quadratic Formula

Subtract 7x from both sides.

$$12x^{2}-7x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, -7 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 12}$$

Take the square root of \left(-7\right)^{2}.

$$x=\frac{-\left(-7\right)±7}{2\times 12}$$

The opposite of -7 is 7.

$$x=\frac{7±7}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{7±7}{24}$$

Now solve the equation x=\frac{7±7}{24} when ± is plus. Add 7 to 7.

$$x=\frac{14}{24}$$

Reduce the fraction \frac{14}{24} to lowest terms by extracting and canceling out 2.

$$x=\frac{7}{12}$$

Now solve the equation x=\frac{7±7}{24} when ± is minus. Subtract 7 from 7.

$$x=\frac{0}{24}$$

Divide 0 by 24.

$$x=0$$

The equation is now solved.

$$x=\frac{7}{12} x=0$$

Steps for Completing the Square

Subtract 7x from both sides.

$$12x^{2}-7x=0$$

Divide both sides by 12.

$$\frac{12x^{2}-7x}{12}=\frac{0}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x^{2}-\frac{7}{12}x=\frac{0}{12}$$

Divide 0 by 12.

$$x^{2}-\frac{7}{12}x=0$$

Divide -\frac{7}{12}, the coefficient of the x term, by 2 to get -\frac{7}{24}. Then add the square of -\frac{7}{24} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{12}x+\left(-\frac{7}{24}\right)^{2}=\left(-\frac{7}{24}\right)^{2}$$

Square -\frac{7}{24} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{12}x+\frac{49}{576}=\frac{49}{576}$$

Factor x^{2}-\frac{7}{12}x+\frac{49}{576}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{24}\right)^{2}=\frac{49}{576}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{24}\right)^{2}}=\sqrt{\frac{49}{576}}$$

Simplify.

$$x-\frac{7}{24}=\frac{7}{24} x-\frac{7}{24}=-\frac{7}{24}$$

Add \frac{7}{24} to both sides of the equation.

$$x=\frac{7}{12} x=0$$