Questions: Use the quadratic formula to solve the equation. 3x^2 + 4x - 3 = 0 The solution set is

Solution Steps

To solve the quadratic equation $3x^2 + 4x - 3 = 0$ using the quadratic formula, we need to identify the coefficients $a$, $b$, and $c$ from the equation $ax^2 + bx + c = 0$. Then, we apply the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ to find the solutions.

1. Identify the coefficients $a$, $b$, and $c$ from the equation.
2. Compute the discriminant $\Delta = b^2 - 4ac$.
3. Use the quadratic formula to find the solutions for $x$.

The given quadratic equation is $3x^2 + 4x - 3 = 0$. Here, the coefficients are:

• $a = 3$
• $b = 4$
• $c = -3$

We calculate the discriminant $\Delta$ using the formula: $$\Delta = b^2 - 4ac$$ Substituting the values: $$\Delta = 4^2 - 4 \cdot 3 \cdot (-3) = 16 + 36 = 52$$

Using the quadratic formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$, we find the solutions: $$x_1 = \frac{-4 + \sqrt{52}}{2 \cdot 3} \quad \text{and} \quad x_2 = \frac{-4 - \sqrt{52}}{2 \cdot 3}$$ Calculating these values: $$x_1 = \frac{-4 + 2\sqrt{13}}{6} = \frac{-2 + \sqrt{13}}{3} \approx 0.5352$$ $$x_2 = \frac{-4 - 2\sqrt{13}}{6} = \frac{-2 - \sqrt{13}}{3} \approx -1.8685$$

Final Answer