Final answer:
To write the equation in standard form, combine like terms to get 5x² - 2x + 12 = 0. The correct answer is Option B: 5x² + 2x - 12 = 0.
Step-by-step explanation:
To write the given equation in standard form, we first need to move all terms to one side of the equation. Starting with the equation -x + 12 + 5x² = -3x, we can add x to both sides to get rid of the -x on the left side and also add 3x to both sides to bring the -3x from the right side to the left. This gives us:
5x² + x + 12 = 0
Next, we can subtract 3x from both sides to combine like terms:
5x² - 2x + 12 = 0
Now the equation is in standard form ax² + bx + c = 0, with a = 5, b = -2, and c = 12. Therefore, the correct answer is Option B: 5x² + 2x - 12 = 0.