1. Let's start by stating the problem: You asked for a "bit more complex" math problem, so I will provide and solve a quadratic equation example. 2. Consider the quadratic equation $$2x^2 - 5x + 3 = 0$$. 3. 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 equation $ax^2 + bx + c = 0$. 4. For our equation, $a=2$, $b=-5$, and $c=3$. 5. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 2 \times 3 = 25 - 24 = 1$$ 6. Since the discriminant is positive, there are two real roots. 7. Substitute values into the quadratic formula: $$x = \frac{-(-5) \pm \sqrt{1}}{2 \times 2} = \frac{5 \pm 1}{4}$$ 8. Calculate the two roots: - $$x_1 = \frac{5 + 1}{4} = \frac{6}{4} = 1.5$$ - $$x_2 = \frac{5 - 1}{4} = \frac{4}{4} = 1$$ 9. Therefore, the solutions to the equation $$2x^2 - 5x + 3 = 0$$ are $$x = 1.5$$ and $$x = 1$$. This completes the solution with detailed steps and explanations.