Solve 4/5x*1.2=3/4x^2

$$\frac{ 4 }{ 5 } x \times 1.2= \frac{ 3 }{ 4 } { x }^{ 2 }$$

Solve for x

$$x=1.28$$

$$x=0$$

Steps Using Factoring

Multiply \frac{4}{5} and 1.2 to get \frac{24}{25}.

$$\frac{24}{25}x=\frac{3}{4}x^{2}$$

Subtract \frac{3}{4}x^{2} from both sides.

$$\frac{24}{25}x-\frac{3}{4}x^{2}=0$$

Factor out x.

$$x\left(\frac{24}{25}-\frac{3}{4}x\right)=0$$

To find equation solutions, solve x=0 and \frac{24}{25}-\frac{3x}{4}=0.

$$x=0 x=\frac{32}{25}$$

Steps Using the Quadratic Formula

Multiply \frac{4}{5} and 1.2 to get \frac{24}{25}.

$$\frac{24}{25}x=\frac{3}{4}x^{2}$$

Subtract \frac{3}{4}x^{2} from both sides.

$$\frac{24}{25}x-\frac{3}{4}x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-\frac{3}{4}x^{2}+\frac{24}{25}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{3}{4} for a, \frac{24}{25} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{24}{25}±\sqrt{\left(\frac{24}{25}\right)^{2}}}{2\left(-\frac{3}{4}\right)}$$

Take the square root of \left(\frac{24}{25}\right)^{2}.

$$x=\frac{-\frac{24}{25}±\frac{24}{25}}{2\left(-\frac{3}{4}\right)}$$

Multiply 2 times -\frac{3}{4}.

$$x=\frac{-\frac{24}{25}±\frac{24}{25}}{-\frac{3}{2}}$$

Now solve the equation x=\frac{-\frac{24}{25}±\frac{24}{25}}{-\frac{3}{2}} when ± is plus. Add -\frac{24}{25} to \frac{24}{25} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 0 by -\frac{3}{2} by multiplying 0 by the reciprocal of -\frac{3}{2}.

$$x=0$$

Now solve the equation x=\frac{-\frac{24}{25}±\frac{24}{25}}{-\frac{3}{2}} when ± is minus. Subtract \frac{24}{25} from -\frac{24}{25} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{48}{25}}{-\frac{3}{2}}$$

Divide -\frac{48}{25} by -\frac{3}{2} by multiplying -\frac{48}{25} by the reciprocal of -\frac{3}{2}.

$$x=\frac{32}{25}$$

The equation is now solved.

$$x=0 x=\frac{32}{25}$$

Steps for Completing the Square

Multiply \frac{4}{5} and 1.2 to get \frac{24}{25}.

$$\frac{24}{25}x=\frac{3}{4}x^{2}$$

Subtract \frac{3}{4}x^{2} from both sides.

$$\frac{24}{25}x-\frac{3}{4}x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-\frac{3}{4}x^{2}+\frac{24}{25}x=0$$

Divide both sides of the equation by -\frac{3}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{4}x^{2}+\frac{24}{25}x}{-\frac{3}{4}}=\frac{0}{-\frac{3}{4}}$$

Dividing by -\frac{3}{4} undoes the multiplication by -\frac{3}{4}.

$$x^{2}+\frac{\frac{24}{25}}{-\frac{3}{4}}x=\frac{0}{-\frac{3}{4}}$$

Divide \frac{24}{25} by -\frac{3}{4} by multiplying \frac{24}{25} by the reciprocal of -\frac{3}{4}.

$$x^{2}-\frac{32}{25}x=\frac{0}{-\frac{3}{4}}$$

Divide 0 by -\frac{3}{4} by multiplying 0 by the reciprocal of -\frac{3}{4}.

$$x^{2}-\frac{32}{25}x=0$$

Divide -\frac{32}{25}, the coefficient of the x term, by 2 to get -\frac{16}{25}. Then add the square of -\frac{16}{25} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{32}{25}x+\left(-\frac{16}{25}\right)^{2}=\left(-\frac{16}{25}\right)^{2}$$

Square -\frac{16}{25} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{32}{25}x+\frac{256}{625}=\frac{256}{625}$$

Factor x^{2}-\frac{32}{25}x+\frac{256}{625}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{16}{25}\right)^{2}=\frac{256}{625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{16}{25}\right)^{2}}=\sqrt{\frac{256}{625}}$$

Simplify.

$$x-\frac{16}{25}=\frac{16}{25} x-\frac{16}{25}=-\frac{16}{25}$$

Add \frac{16}{25} to both sides of the equation.

$$x=\frac{32}{25} x=0$$