PSAT Math Multiple-Choice Question 676: Answer and Explanation

Question: 676

What are the solutions to 21x² = 15x + 18?

• A.
• B.
• C.
• D. No real solutions

Correct Answer: A

Explanation:

(A) To find the solutions, subtract 15x and 18 from both sides to get everything on the left side:

21x² - 15x -18 = 0

Next, factor out a 3 to make the quadratic equation a bit simpler:

3(7x² - 5x - 6) = 0

Divide both sides by 3:

7x² - 5x - 6 = 0

Notice that the answer choices look similar in structure to the quadratic formula . This suggests that we try to factor our quadratic equation using the quadratic formula. Letting a = 7, b = -5, and c = -6 in the quadratic formula above, we get choice (A).