1. Let's start by stating the problem: We want to solve a more difficult algebraic equation or expression to practice. 2. A good way to increase difficulty is to include quadratic expressions, factoring, and solving for variables. 3. For example, consider the equation $$2x^2 - 5x + 3 = 0$$. 4. The formula to solve quadratic equations is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients from the quadratic equation $ax^2 + bx + c = 0$. 5. Here, $a=2$, $b=-5$, and $c=3$. 6. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 2 \times 3 = 25 - 24 = 1$$. 7. Since the discriminant is positive, there are two real solutions. 8. Substitute into the quadratic formula: $$x = \frac{-(-5) \pm \sqrt{1}}{2 \times 2} = \frac{5 \pm 1}{4}$$. 9. Calculate each solution: - $$x_1 = \frac{5 + 1}{4} = \frac{6}{4} = 1.5$$ - $$x_2 = \frac{5 - 1}{4} = \frac{4}{4} = 1$$ 10. Therefore, the solutions to the equation are $$x = 1.5$$ and $$x = 1$$. This problem is more challenging than simple linear equations and helps practice quadratic solving techniques.