Solve 5x(x+3)/4=x/2

$$\frac { 5 x ( x + 3 ) } { 4 } = \frac { x } { 2 }$$

Solve for x

$$x = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

$$x=0$$

Steps Using Factoring

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$5x\left(x+3\right)=2x$$

Use the distributive property to multiply 5x by x+3.

$$5x^{2}+15x=2x$$

Subtract 2x from both sides.

$$5x^{2}+15x-2x=0$$

Combine 15x and -2x to get 13x.

$$5x^{2}+13x=0$$

Factor out x.

$$x\left(5x+13\right)=0$$

To find equation solutions, solve x=0 and 5x+13=0.

$$x=0 x=-\frac{13}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$5x\left(x+3\right)=2x$$

Use the distributive property to multiply 5x by x+3.

$$5x^{2}+15x=2x$$

Subtract 2x from both sides.

$$5x^{2}+15x-2x=0$$

Combine 15x and -2x to get 13x.

$$5x^{2}+13x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 13 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-13±\sqrt{13^{2}}}{2\times 5}$$

Take the square root of 13^{2}.

$$x=\frac{-13±13}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-13±13}{10}$$

Now solve the equation x=\frac{-13±13}{10} when ± is plus. Add -13 to 13.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

Now solve the equation x=\frac{-13±13}{10} when ± is minus. Subtract 13 from -13.

$$x=-\frac{26}{10}$$

Reduce the fraction \frac{-26}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{13}{5}$$

The equation is now solved.

$$x=0 x=-\frac{13}{5}$$

Steps for Completing the Square

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$5x\left(x+3\right)=2x$$

Use the distributive property to multiply 5x by x+3.

$$5x^{2}+15x=2x$$

Subtract 2x from both sides.

$$5x^{2}+15x-2x=0$$

Combine 15x and -2x to get 13x.

$$5x^{2}+13x=0$$

Divide both sides by 5.

$$\frac{5x^{2}+13x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\frac{13}{5}x=\frac{0}{5}$$

Divide 0 by 5.

$$x^{2}+\frac{13}{5}x=0$$

Divide \frac{13}{5}, the coefficient of the x term, by 2 to get \frac{13}{10}. Then add the square of \frac{13}{10} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{13}{5}x+\left(\frac{13}{10}\right)^{2}=\left(\frac{13}{10}\right)^{2}$$

Square \frac{13}{10} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{13}{5}x+\frac{169}{100}=\frac{169}{100}$$

Factor x^{2}+\frac{13}{5}x+\frac{169}{100}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{13}{10}\right)^{2}=\frac{169}{100}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{13}{10}\right)^{2}}=\sqrt{\frac{169}{100}}$$

Simplify.

$$x+\frac{13}{10}=\frac{13}{10} x+\frac{13}{10}=-\frac{13}{10}$$

Subtract \frac{13}{10} from both sides of the equation.

$$x=0 x=-\frac{13}{5}$$