Final answer:
The quadratic equation 3x² + 9x + 4 = 0 is solved using the quadratic formula, which yields two solutions for x: −(9) + √(33) / 6 and −(9) - √(33) / 6.
Step-by-step explanation:
To solve the quadratic equation 3x² + 9x + 4 = 0 using the quadratic formula, we must first identify the coefficients of the equation which are a = 3, b = 9, and c = 4. The quadratic formula is given by:
x = −b ± √(b² - 4ac) / (2a)
Plugging our coefficients into the formula gives us:
x = −(9) ± √((9)² - 4(3)(4)) / (2(3))
x = −(9) ± √(81 - 48) / 60
x = −(9) ± √(33) / 6
Therefore, the solutions for x are:
x = −(9) + √(33) / 6, and x = −(9) - √(33) / 6
These are the two possible solutions for x in the quadratic equation 3x²+9x+4=0.