Final answer:
The problem is a complex equation, which we rewrite as 8/x = 3x + 9, and then rearranged to get 3x^2 + 9x - 8 = 0. This is a quadratic equation that can be solved by factoring or using the quadratic formula.
Step-by-step explanation:
The subject of this question is Mathematics, specifically, it involves solving a complex equation. The student's equation is 9 less than the quotient of 8 and x equals the product of 3 and x. Rewritten, this equation is (8/x) - 9 = 3x.
We begin by isolating the variables. First, we rearrange the equation to get the x terms on one side, by adding 9 to both sides. This gives us (8/x) = 3x + 9. Next, we can multiply every term by x to clear out the denominator, making our equation 8 = 3x^2 + 9x.
Subtract 8 from both sides to get 3x^2 + 9x - 8 = 0. This is now a quadratic equation, which can be factored or solved using the quadratic formula: x = [ -b ± sqrt(b^2 - 4ac) ] / 2a
Learn more about Complex Equation