Answer:
The solution of the given equation are [tex]x=\frac{-2-\sqrt{10}}{3}[/tex] and [tex]x=\frac{-2+\sqrt{10}}{3}[/tex].
Step-by-step explanation:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The given quadratic equation is
[tex]3x^2+4x-2=0[/tex]
Here, [tex]a=3,b=4,c=-2[/tex]
Using quadratic formula, we get
[tex]x=\frac{-4\pm \sqrt{4^2-4(3)(-2)}}{2(3)}[/tex]
[tex]x=\frac{-4\pm \sqrt{40}}{6}[/tex]
[tex]x=\frac{-4\pm 2\sqrt{10}}{6}[/tex]
[tex]x=\frac{-2\pm \sqrt{10}}{3}[/tex]
Therefore the solution of the given equation are [tex]x=\frac{-2-\sqrt{10}}{3}[/tex] and [tex]x=\frac{-2+\sqrt{10}}{3}[/tex].
