Final answer:
To solve the given literal equation for a, multiply both sides by ka to get rid of the fraction, move terms to one side to form a quadratic equation, then apply the quadratic formula.
Step-by-step explanation:
To solve the literal equation u = -2a - 3/(ka) for a, follow these steps:
- Multiply both sides of the equation by ka to eliminate the fraction: u × ka = (-2a - 3/ka) × ka. This simplifies to uka = -2a² - 3.
- To isolate the term containing a², move uka to the other side by adding uka to both sides: uka + 2a² = -3.
- Now you have a quadratic equation in terms of a. You can re-arrange it to 2a² + uka + 3 = 0. Use the quadratic formula where a = (-b ± √(b² - 4ac))/(2a) with a=2, b=uk, and c=3 to find the values of a.
- Finally, solve for the positive and negative values of a, if they exist.
Remember that some quadratic equations might result in complex solutions depending on the value of the discriminant b² - 4ac.