Answer :
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex]x = \frac{-(-8) +/- \sqrt{(-8)^2 - 4(3)(2)}}{2(3)} [/tex]
[tex] x = \frac{8 +/- \sqrt{64 - 24}}{6} [/tex]
[tex]x = \frac{8 +/- \sqrt{40}}{6} [/tex]
[tex]x = \frac{8 +/- 6.31}{6} [/tex]
[tex]x = \frac{14.32}{6} [/tex] x ≈ 2.39
[tex]x = \frac{1.68}{6} [/tex] x ≈ 0.28
[tex]3x^2 - 8x + 2 = 0\\ \\a=3 , \ \ b=-8 , \ \ c=2 \\ \\x_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a} =\frac{8-\sqrt{ (-8)^2-4 \cdot 3\cdot 2}}{2 \cdot 3} =\frac{8-\sqrt{ 64-24 }}{6} =\\ \\ =\frac{8-\sqrt{40 }}{6} = \frac{ 8-\sqrt{4\cdot 10 } }{6} = \frac{ 8-2\sqrt{ 10 }}{6} = \frac{2 (4-\sqrt{ 10 })}{6} = \frac{ 4-\sqrt{ 10 } }{3}[/tex]
[tex]x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a} =\frac{8+\sqrt{ (-8)^2-4 \cdot 3\cdot 2}}{2 \cdot 3} = \frac{ 4+\sqrt{ 10 } }{3}[/tex]
[tex]x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a} =\frac{8+\sqrt{ (-8)^2-4 \cdot 3\cdot 2}}{2 \cdot 3} = \frac{ 4+\sqrt{ 10 } }{3}[/tex]
