Question

Which of the following values of x satisfy the equation 3x^2-8x+4=0

Answer 1

Hey there :)

3x² - 8x + 4 = 0

Divide into 2 groups

3x² - 6x - 2x + 4
3x ( x - 2 ) - 2 ( x - 2 ) = 0
          ↓               ↓
     Factor out the GCF

               x = 2
                  ↑
( 3x - 2 )( x - 2 ) = 0
    ↓
x = $\frac{2}{3}$  


2 values satisfy x = $\frac{2}{3} , 2$

Answer 2

$3x^2-8x+4=0\\\\\Delta=b^2-4ac=(-8)^2-4\times3\times4=64-48=16\\\\x_1=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{8-4}{6}=\dfrac{4}{6}=\dfrac{2}{3}\\\\x_2=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{8+4}{6}=\dfrac{12}{6}=2\\\\\boxed{S=\left\{\dfrac{2}{3};2\right\}}$