Answer:

To transform the quadratic equation ³/4x² - ⁷/8x - ¹/6 = 0 into the standard form ax² + bx + c = 0 and solve it, we'll need to make the denominators equal and get rid of the fractions.

To make the denominators equal, we can multiply every term in the equation by the least common denominator (LCD) of 24. This will help us eliminate the fractions.

First, let's multiply every term in the equation by 24 to clear the fractions:

24 * (³/4x²) - 24 * (⁷/8x) - 24 * (¹/6) = 24 * 0

6x² - 14x - 4 = 0

Now the quadratic equation is in standard form ax² + bx + c = 0, where a = 6, b = -14, and c = -4. We can solve it by factoring, completing the square, or using the quadratic formula.

In this case, let's solve it using factoring:

6x² - 14x - 4 = 0

2(3x² - 7x - 2) = 0

Now let's factor the quadratic expression inside the parentheses:

2(3x + 1)(x - 2) = 0

Setting each factor equal to zero:

3x + 1 = 0 or x - 2 = 0

Solving each equation separately:

For 3x + 1 = 0:

3x = -1

x = -1/3

For x - 2 = 0:

x = 2

Therefore, the solutions to the quadratic equation are x = -1/3 and x = 2.