Solve Using the Quadratic Formula 6/x=7-2x

$\frac{6}{x} = 7 - 2 x$

Move all the expressions to the left side of the equation.

Subtract $7$ from both sides of the equation.

$\frac{6}{x} - 7 = - 2 x$

Add $2 x$ to both sides of the equation.

$\frac{6}{x} - 7 + 2 x = 0$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1, 1, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $\frac{6}{x} - 7 + 2 x = 0$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{6}{x} - 7 + 2 x = 0$ by $x$ .

$\frac{6}{x} x - 7 x + 2 x \cdot x = 0 x$

Simplify the left side.

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{6}{x} x - 7 x + 2 x \cdot x = 0 x$

Rewrite the expression.

$6 - 7 x + 2 x \cdot x = 0 x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$6 - 7 x + 2 (x \cdot x) = 0 x$

Multiply $x$ by $x$ .

$6 - 7 x + 2 x^{2} = 0 x$

Simplify the right side.

Multiply $0$ by $x$ .

$6 - 7 x + 2 x^{2} = 0$

Solve the equation.

Factor by grouping.

Reorder terms.

$2 x^{2} - 7 x + 6 = 0$

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 6 = 12$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$2 x^{2} - 7 x + 6 = 0$

Rewrite $- 7$ as $- 3$ plus $- 4$

$2 x^{2} + (- 3 - 4) x + 6 = 0$

Apply the distributive property.

$2 x^{2} - 3 x - 4 x + 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) - 4 x + 6 = 0$

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 3) - 2 (2 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (x - 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 3 = 0$

$x - 2 = 0$

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $(2 x - 3) (x - 2) = 0$ true.

$x = \frac{3}{2}, 2$

Solve Using the Quadratic Formula 6/x=7-2x

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