Let's solve the equation step by step:

Given equation: $4x^2 - 9 + 3 = 0$

Step 1: Simplify the equation

Combine like terms: $4x^2 - 6 = 0$

Step 2: Isolate $x^2$

Add 6 to both sides: $4x^2 = 6$

Step 3: Solve for $x^2$

Divide both sides by 4: $x^2 = \frac{6}{4} = \frac{3}{2}$

Step 4: Solve for $x$

Take the square root of both sides: $x = \pm \sqrt{\frac{3}{2}} = \pm \frac{\sqrt{6}}{2}$

Final Answer:

$x = \pm \frac{\sqrt{6}}{2}$

Would you like further details on any of the steps?

Here are 5 related questions:

1. How do you solve quadratic equations by factoring?
2. What is the difference between solving by factoring and using the quadratic formula?
3. How do you simplify square roots involving fractions?
4. What are the properties of square roots of negative numbers?
5. How do you check if a solution is correct in a quadratic equation?

Tip: Always simplify your equation as much as possible before solving for the variable!