1. Let's state the problem: Solve the quadratic equation $$2x^2 - 5x + 2 = 0$$. 2. Identify coefficients: Here, $$a=2$$, $$b=-5$$, and $$c=2$$. 3. Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ to find the roots. 4. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 2 \times 2 = 25 - 16 = 9$$ 5. Substitute values into the quadratic formula: $$x = \frac{-(-5) \pm \sqrt{9}}{2 \times 2} = \frac{5 \pm 3}{4}$$ 6. Calculate both roots: - $$x_1 = \frac{5 + 3}{4} = \frac{8}{4} = 2$$ - $$x_2 = \frac{5 - 3}{4} = \frac{2}{4} = 0.5$$ 7. Therefore, the solutions of the quadratic equation are $$x = 2$$ and $$x = 0.5$$.