Final answer:
To solve the quadratic equation y = 2x^2 - 9x + 5, we can use the quadratic formula. The solutions for x are (9 + √41) / 4 and (9 - √41) / 4.
Step-by-step explanation:
To find the solutions of the quadratic equation, y = 2x^2 - 9x + 5, we can apply the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula x = (-b ± √(b^2 - 4ac)) / (2a).
In this equation, a = 2, b = -9, and c = 5. Plugging these values into the quadratic formula gives us x = (-(-9) ± √((-9)^2 - 4 * 2 * 5)) / (2 * 2), which simplifies to x = (9 ± √(81 - 40)) / 4.
Therefore, the solutions for y = 2x^2 - 9x + 5 are x = (9 + √41) / 4 and x = (9 - √41) / 4.