Final answer:
The equation y(4) - y = 0 is a quadratic equation. The solutions can be found using the quadratic formula.
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)
Plugging in the values, we get:
x = (-(-14.3) ± √((-14.3)² - 4(4.90)(-20.0))) / (2(4.90))
After simplifying and evaluating, we find two solutions:
x ≈ 3.2337 or x ≈ -1.2407
This quadratic equation solution underscores the value of the quadratic formula in obtaining precise solutions for equations in this format, fundamental in mathematical analysis, modeling various phenomena, and resolving equations in physics, engineering, and diverse scientific disciplines.