Final answer:
The question involves solving a quadratic equation by rearranging it to zero and applying the quadratic formula. The solutions to the equation 15x^2 - 12x - 31 = 6x - 7 are found by calculating the values of x using the quadratic formula with a = 15, b = -18, and c = -24.
Step-by-step explanation:
The student's question asks about solving a quadratic equation in the form of 15x2 - 12x - 31 = 6x - 7. To find the solutions to this equation, we first need to set it to zero by moving all terms to one side, resulting in 15x2 - 18x - 24 = 0. We then solve the equation using the quadratic formula, which in general is used to solve equations of the form ax2 + bx + c = 0.
To apply the quadratic formula, identify a, b, and c from the equation: a = 15, b = -18, and c = -24. Substitute these values into the quadratic formula x = (-b ± √(b2 - 4ac)) / (2a) and calculate to find the two possible values of x. These values will be the solutions to the quadratic equation.