we know that for
[tex]a{x}^{2} + bx + c = 0[/tex]
the roots are:
[tex] x1 = \frac{ - b + \sqrt{ { {b}^{2} } - 4ac} }{2a} [/tex]
and
[tex] x2 = \frac{ - b - \sqrt{ { {b}^{2} } - 4ac} }{2a} [/tex]
so putting into the formula we get:
[tex]3 {x}^{2} + 4x - 2 = 0[/tex]
and
[tex]{{b}^{2} } - 4ac = {4}^{2} - 4 \times 3 \times ( - 2) = \\ 16 + 24 = 40[/tex]
so:
[tex]x1 = \frac{ - 4 + \sqrt{40} }{2 \times 3} = \frac{ - 2 + \sqrt{10} }{3} [/tex]
and
[tex]x2 = \frac{ - 4 - \sqrt{40} }{2 \times 3} = \frac{ - 2 - \sqrt{10}}{3}[/tex]
