Final answer:
The equation is a quadratic equation in the form of at² + bt + c = 0, where a = 24, b = 0, and c = -24. Using the quadratic formula, we find that x = ±1.
Step-by-step explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = 14.3, and c = -20.0. Its solutions are given by the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, we have x³ - 1 = y² / 24. To rewrite this in the form of a quadratic equation, we can multiply both sides by 24 to get 24x³ - 24 = y². Now we can rearrange the equation as 24x³ - y² = 24. Comparing this equation with the standard form, we have a = 24, b = 0, and c = -24. Plugging these values into the quadratic formula, we get:
x = ±√(0² - 4 * 24 * -24) / (2 * 24) = ±√(0 + 2304) / 48 = ±√(2304) / 48 = ±48 / 48 = ±1