Question

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

Explanation:

Step1: Identify a,b,c values

For $ax^2+bx+c=0$, $a=4$, $b=-9$, $c=3$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$b^2-4ac=(-9)^2-4(4)(3)=81-48=33$

Step4: Substitute into formula

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

Answer:

$x=\frac{9+\sqrt{33}}{8}, \frac{9-\sqrt{33}}{8}$