Question

Solve the equation \(4x^2 - 9x + 3 = 0\), using quadratic formula.

Answer 1

Solving the Quadratic Equation

The given equation is:

\[ 4x^2 - 9x + 3 = 0 \]

This is in the form \( ax^2 + bx + c = 0 \), where:

• \( a = 4 \)
• \( b = -9 \)
• \( c = 3 \)

Step 1: Use the Quadratic Formula

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Step 2: Calculate the Discriminant

\[ D = b^2 - 4ac = (-9)^2 - 4(4)(3) = 81 - 48 = 33 \]

Step 3: Substitute into the Formula

\[ x = \frac{-(-9) \pm \sqrt{33}}{2 \cdot 4} = \frac{9 \pm \sqrt{33}}{8} \]

Final Answer:

The two solutions are: \[ x = \frac{9 + \sqrt{33}}{8} \quad \text{or} \quad x = \frac{9 - \sqrt{33}}{8} \] or compactly, \[ \boxed{x = \frac{9 \pm \sqrt{33}}{8}} \]