Question

use the quadratic formula to solve for x.
$3x^2 - 9x + 4 = 0$
(if there is more than one solution, separate them with commas.)
$x = \square$

Explanation:

Step1: Identify coefficients

For \(3x^2 - 9x + 4 = 0\), \(a = 3\), \(b = -9\), \(c = 4\).

Step2: Apply quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Substitute values: \(x=\frac{-(-9)\pm\sqrt{(-9)^2 - 4(3)(4)}}{2(3)}\).

Step3: Simplify discriminant

Calculate \(b^2 - 4ac\): \(81 - 48 = 33\).

Step4: Solve for x

\(x=\frac{9\pm\sqrt{33}}{6}\).

Answer:

\(\frac{9 + \sqrt{33}}{6}, \frac{9 - \sqrt{33}}{6}\)