$3{x}^{2}+4x-2=0$

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Quadratic Formula

Complete the Square

Use the Quadratic Formula.

In general, given

a{x}^{2}+bx+c=0

, there exists two solutions where:

x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}

In this case,

a=3

b=4

and

c=-2

{x}^{}=\frac{-4+\sqrt{{4}^{2}-4\times 3\times -2}}{2\times 3},\frac{-4-\sqrt{{4}^{2}-4\times 3\times -2}}{2\times 3}

Simplify.

x=\frac{-4+2\sqrt{10}}{6},\frac{-4-2\sqrt{10}}{6}

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x=\frac{-4+2\sqrt{10}}{6},\frac{-4-2\sqrt{10}}{6}

Simplify solutions.

x=-\frac{2-\sqrt{10}}{3},-\frac{2+\sqrt{10}}{3}

Done

Decimal Form: 0.387426, -1.720759

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3x2+4x−2=03{x}^{2}+4x-2=03x2+4x−2=0