Solve 3+8/x/frac{2{x}}=10

$$\frac { 3 + \frac { 8 } { x } } { \frac { 2 } { x } } = 10$$

Solve for x

$$x=4$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Divide 3+\frac{8}{x} by \frac{2}{x} by multiplying 3+\frac{8}{x} by the reciprocal of \frac{2}{x}.

$$\frac{\left(3+\frac{8}{x}\right)x}{2}=10$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\frac{\left(\frac{3x}{x}+\frac{8}{x}\right)x}{2}=10$$

Since \frac{3x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3x+8}{x}x}{2}=10$$

Express \frac{3x+8}{x}x as a single fraction.

$$\frac{\frac{\left(3x+8\right)x}{x}}{2}=10$$

Use the distributive property to multiply 3x+8 by x.

$$\frac{\frac{3x^{2}+8x}{x}}{2}=10$$

Multiply both sides by 2.

$$\frac{3x^{2}+8x}{x}=10\times 2$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3x^{2}+8x=10\times 2x$$

Multiply 10 and 2 to get 20.

$$3x^{2}+8x=20x$$

Subtract 20x from both sides.

$$3x^{2}+8x-20x=0$$

Combine 8x and -20x to get -12x.

$$3x^{2}-12x=0$$

Factor out x.

$$x\left(3x-12\right)=0$$

To find equation solutions, solve x=0 and 3x-12=0.

$$x=0 x=4$$

Variable x cannot be equal to 0.

$$x=4$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Divide 3+\frac{8}{x} by \frac{2}{x} by multiplying 3+\frac{8}{x} by the reciprocal of \frac{2}{x}.

$$\frac{\left(3+\frac{8}{x}\right)x}{2}=10$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\frac{\left(\frac{3x}{x}+\frac{8}{x}\right)x}{2}=10$$

Since \frac{3x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3x+8}{x}x}{2}=10$$

Express \frac{3x+8}{x}x as a single fraction.

$$\frac{\frac{\left(3x+8\right)x}{x}}{2}=10$$

Use the distributive property to multiply 3x+8 by x.

$$\frac{\frac{3x^{2}+8x}{x}}{2}=10$$

Subtract 10 from both sides.

$$\frac{\frac{3x^{2}+8x}{x}}{2}-10=0$$

Multiply both sides of the equation by 2.

$$\frac{3x^{2}+8x}{x}-20=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3x^{2}+8x+x\left(-20\right)=0$$

Combine 8x and x\left(-20\right) to get -12x.

$$3x^{2}-12x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -12 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 3}$$

Take the square root of \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\times 3}$$

The opposite of -12 is 12.

$$x=\frac{12±12}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{12±12}{6}$$

Now solve the equation x=\frac{12±12}{6} when ± is plus. Add 12 to 12.

$$x=\frac{24}{6}$$

Divide 24 by 6.

$$x=4$$

Now solve the equation x=\frac{12±12}{6} when ± is minus. Subtract 12 from 12.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

The equation is now solved.

$$x=4 x=0$$

Variable x cannot be equal to 0.

$$x=4$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Divide 3+\frac{8}{x} by \frac{2}{x} by multiplying 3+\frac{8}{x} by the reciprocal of \frac{2}{x}.

$$\frac{\left(3+\frac{8}{x}\right)x}{2}=10$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\frac{\left(\frac{3x}{x}+\frac{8}{x}\right)x}{2}=10$$

Since \frac{3x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3x+8}{x}x}{2}=10$$

Express \frac{3x+8}{x}x as a single fraction.

$$\frac{\frac{\left(3x+8\right)x}{x}}{2}=10$$

Use the distributive property to multiply 3x+8 by x.

$$\frac{\frac{3x^{2}+8x}{x}}{2}=10$$

Multiply both sides by 2.

$$\frac{3x^{2}+8x}{x}=10\times 2$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3x^{2}+8x=10\times 2x$$

Multiply 10 and 2 to get 20.

$$3x^{2}+8x=20x$$

Subtract 20x from both sides.

$$3x^{2}+8x-20x=0$$

Combine 8x and -20x to get -12x.

$$3x^{2}-12x=0$$

Divide both sides by 3.

$$\frac{3x^{2}-12x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\left(-\frac{12}{3}\right)x=\frac{0}{3}$$

Divide -12 by 3.

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

Divide 0 by 3.

$$x^{2}-4x=0$$

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

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

Square -2.

$$x^{2}-4x+4=4$$

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

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

Take the square root of both sides of the equation.

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

Simplify.

$$x-2=2 x-2=-2$$

Add 2 to both sides of the equation.

$$x=4 x=0$$

Variable x cannot be equal to 0.

$$x=4$$