Solve the equation $4x^2 - 9x + 3 = 0$, using quadratic formula

Solve the equation $4x^2 - 9x + 3 = 0$, using quadratic formula

We are given the quadratic equation:

$ \displaystyle 4x^2 - 9x + 3 = 0 $

### Step 1: Identify Coefficients
Comparing with the standard quadratic equation $ax^2 + bx + c = 0$:

$ a = 4, \quad b = -9, \quad c = 3 $

### Step 2: Apply the Quadratic Formula
The quadratic formula is:

$ \displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Substituting the values of $a$, $b$, and $c$:

$ \displaystyle x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(4)(3)}}{2(4)} $

$ \displaystyle = \frac{9 \pm \sqrt{81 - 48}}{8} $

$ \displaystyle = \frac{9 \pm \sqrt{33}}{8} $

### Final Answer: $ \displaystyle x = \frac{9 + \sqrt{33}}{8}, \quad x = \frac{9 - \sqrt{33}}{8} $

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