To solve this, we need to use the quadratic formula.
When we have an equation of the form:
[tex]ax^2+bx+c=0[/tex]
We can use:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]
In this case, we have the equation:
[tex]3x^2-8x+4=0[/tex]
With:
a = 3
b = -8
c = 4
Then:
[tex]x_{1,2}=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot3\cdot4}}{2\cdot3}[/tex]
THen solve:
[tex]\begin{gathered} x_{1,2}=\frac{8\pm\sqrt[]{64^{}-48}}{6} \\ x_{1,2}=\frac{8\pm\sqrt[]{16}}{6} \\ x_{1,2}=\frac{8\pm4}{6} \end{gathered}[/tex]
THen the two solutions are:
[tex]\begin{gathered} x_1=\frac{8+4}{6}=\frac{12}{6}=2 \\ x_2=\frac{8-4}{6}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]
Thus, the correct answer is option A
