$\frac{11 x^{2}}{10}-\frac{3 x}{5}=\frac{x}{2}$

Step 1 ：Move all terms to one side of the equation to get a quadratic equation in the form of $ax^2 + bx + c = 0$: \(\frac{11 x^{2}}{10}-\frac{11 x}{10}=0\)

Step 2 ：Factor out the common term $\frac{11x}{10}$: \(\frac{11x}{10}(x - 1) = 0\)

Step 3 ：Set each factor equal to zero and solve for x: \(\frac{11x}{10} = 0\) and \(x - 1 = 0\)

Step 4 ：Find the solutions: \(x = 0\) and \(x = 1\)

Step 5 ：\(\boxed{x = 0, x = 1}\)