Solve 6+2x+4/3x=8

$$6 + \frac { 2 x + 4 } { 3 } x = 8$$

Solve for x

$$x=-3$$

$$x=1$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$18+\left(2x+4\right)x=24$$

Use the distributive property to multiply 2x+4 by x.

$$18+2x^{2}+4x=24$$

Subtract 24 from both sides.

$$18+2x^{2}+4x-24=0$$

Subtract 24 from 18 to get -6.

$$-6+2x^{2}+4x=0$$

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.

$$2x^{2}+4x-6=0$$

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

$$x=\frac{-4±\sqrt{4^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 2\left(-6\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-4±\sqrt{16-8\left(-6\right)}}{2\times 2}$$

Multiply -8 times -6.

$$x=\frac{-4±\sqrt{16+48}}{2\times 2}$$

Add 16 to 48.

$$x=\frac{-4±\sqrt{64}}{2\times 2}$$

Take the square root of 64.

$$x=\frac{-4±8}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-4±8}{4}$$

Now solve the equation x=\frac{-4±8}{4} when ± is plus. Add -4 to 8.

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

Divide 4 by 4.

$$x=1$$

Now solve the equation x=\frac{-4±8}{4} when ± is minus. Subtract 8 from -4.

$$x=-\frac{12}{4}$$

Divide -12 by 4.

$$x=-3$$

The equation is now solved.

$$x=1 x=-3$$

Steps for Completing the Square

Multiply both sides of the equation by 3.

$$18+\left(2x+4\right)x=24$$

Use the distributive property to multiply 2x+4 by x.

$$18+2x^{2}+4x=24$$

Subtract 18 from both sides.

$$2x^{2}+4x=24-18$$

Subtract 18 from 24 to get 6.

$$2x^{2}+4x=6$$

Divide both sides by 2.

$$\frac{2x^{2}+4x}{2}=\frac{6}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{4}{2}x=\frac{6}{2}$$

Divide 4 by 2.

$$x^{2}+2x=\frac{6}{2}$$

Divide 6 by 2.

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

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=3+1^{2}$$

Square 1.

$$x^{2}+2x+1=3+1$$

Add 3 to 1.

$$x^{2}+2x+1=4$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{4}$$

Simplify.

$$x+1=2 x+1=-2$$

Subtract 1 from both sides of the equation.

$$x=1 x=-3$$