Answer:
The solutions are
[tex]x=1+\sqrt{\frac{7}{3}}[/tex]
[tex]x=1-\sqrt{\frac{7}{3}}[/tex]
Step-by-step explanation:
we have
[tex]3x^{2}-6x-4=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]3x^{2}-6x=4[/tex]
Factor the leading coefficient
[tex]3(x^{2}-2x)=4[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]3(x^{2}-2x+1)=4+3[/tex]
[tex]3(x^{2}-2x+1)=7[/tex]
Rewrite as perfect squares
[tex]3(x-1)^{2}=7[/tex]
[tex](x-1)^{2}=\frac{7}{3}[/tex]
square root both sides
[tex]x-1=(+/-)\sqrt{\frac{7}{3}}[/tex]
[tex]x=1(+/-)\sqrt{\frac{7}{3}}[/tex]
[tex]x=1+\sqrt{\frac{7}{3}}[/tex]
[tex]x=1-\sqrt{\frac{7}{3}}[/tex]
