Final answer:
To solve the quadratic equation 6q^2 + q - 15 = 0, we can rearrange the equation, use the quadratic formula, and simplify the expression to find the solutions for q.
Step-by-step explanation:
This is a quadratic equation. To solve for q, we can rearrange the equation into the standard form: 6q^2 + q - 15 = 0. We can then use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by: x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation, the values of a, b, and c are 6, 1, and -15, respectively. Substituting these values into the quadratic formula, we get: q = (-1 ± √(1^2 - 4(6)(-15))) / (2(6)). Simplifying further, we have: q = (-1 ± √(1 + 360)) / 12. Finally, we can approximate the value of q by calculating the positive and negative solutions using a calculator.