Answer:
[tex]x_{1} = 1+\frac{2\sqrt{6}}{3} \\\\x_{2} = 1-\frac{2\sqrt{6}}{3}[/tex]
Step-by-step explanation:
3x^2 - 6x - 5=0
quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c}}{2*a}[/tex]
a=3 b=-6 c=-5
[tex]x=\frac{-(-6)+-\sqrt{(-6)^{2}-4*3*-5}}{2*3}[/tex]
[tex]x=\frac{6+-\sqrt{36+60}}{6} \\\\x=\frac{6+-\sqrt{96}}{6} \\\\x=\frac{6+-\sqrt{2^{2}*2^{2}*2*3 }}{6} \\\\x=\frac{6+-4\sqrt{6}}{6} \\[/tex]
so we have:
[tex]x_{1} = 1+\frac{2\sqrt{6}}{3} \\\\x_{2} = 1-\frac{2\sqrt{6}}{3}[/tex]
