Solve the following \( \frac{3}{x}+x+2 x=2 \)

Solve the equation \( \frac{3}{x}+x+2x=2 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{3}{x}+x+2x=2\) - step1: Add the terms: \(\frac{3}{x}+3x=2\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{3}{x}+3x\right)x=2x\) - step3: Simplify the equation: \(3+3x^{2}=2x\) - step4: Move the expression to the left side: \(3+3x^{2}-2x=0\) - step5: Rewrite in standard form: \(3x^{2}-2x+3=0\) - step6: Solve using the quadratic formula: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 3\times 3}}{2\times 3}\) - step7: Simplify the expression: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\times 3\times 3}}{6}\) - step8: Simplify the expression: \(x=\frac{2\pm \sqrt{-32}}{6}\) - step9: The expression is undefined: \(x \notin \mathbb{R}\) The equation \( \frac{3}{x}+x+2x=2 \) does not have any real solutions. Therefore, there is no real value of \( x \) that satisfies the equation.