Solve for x. (2)/(x)=3-(7x)/(x-2)

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Write Equation: Write down the equation. We have the equation (2)/(x) = 3 - (7x)/(x-2).Find Common Denominator: Find a common denominator to combine the terms on the right side of the equation. The common denominator for x and (x-2) is x(x-2). We will multiply each term by this common denominator to clear the fractions.Multiply by Common Denominator: Multiply each term by the common denominator x(x-2). (2)/(x) * x(x-2) = 3 * x(x-2) - (7x)/(x-2) * x(x-2)Simplify After Multiplying: Simplify the equation after multiplying. 2(x-2) = 3x(x-2) - 7x(x)Distribute and Expand: Distribute and expand the terms. 2x - 4 = 3x^2 - 6x - 7x^2Combine Like Terms: Combine like terms on the right side of the equation. 2x - 4 = -4x^2 - 6xMove Terms to One Side: Move all terms to one side to set the equation to zero. 4x^2 + 2x - 6x + 4 = 0Combine Like Terms: Combine like terms. 4x^2 - 4x + 4 = 0Solve Quadratic Equation: Solve the quadratic equation. This is a quadratic equation in standard form. We can use the quadratic formula, factoring, or completing the square to find the value of x. However, this equation does not factor nicely, so we will use the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a = 4, b = -4, and c = 4.Apply Quadratic Formula: Apply the quadratic formula. x = [-(-4) ± sqrt((-4)^2 - 4*4*4)] / (2*4) x = [4 ± sqrt(16 - 64)] / 8Calculate Discriminant: Calculate the discriminant (the part under the square root). sqrt(16 - 64) = sqrt(-48) Since the discriminant is negative, there are no real solutions to this equation.

Solve for $x$ . $\newline$ $\frac{2}{x}=3-\frac{7 x}{x-2}$

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Solve for $x$ . $\newline$ $\frac{2}{x}=3-\frac{7 x}{x-2}$