What are the solutions to the equation 3x^2-12x-4=0 ?

The solutions to the equation 3x^2-12x-4=0 are x=(2(3+2sqrt(3)))/3 ,x=(2(3-2sqrt(3)))/3

Find the zeros of 3x^2-12x-4=0

The zeros of 3x^2-12x-4=0 are x=(2(3+2sqrt(3)))/3 ,x=(2(3-2sqrt(3)))/3

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3 x^{2} - 12 x - 4 = 0

x = \frac{2 ( 3 + 2 3 )}{3}, x = \frac{2 ( 3 - 2 3 )}{3}

Decimal Notation

x = 4.30940 \dots, x = - 0.30940 \dots

Solution steps

3 x^{2} - 12 x - 4 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 ( - 4 )}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 (- 4) = 83

x_{1, 2} = \frac{- ( - 12 ) \pm 8 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 8 3}{2 \cdot 3}, x_{2} = \frac{- ( - 12 ) - 8 3}{2 \cdot 3}

x = \frac{- ( - 12 ) + 8 3}{2 \cdot 3} : \frac{2 ( 3 + 2 3 )}{3}

x = \frac{- ( - 12 ) - 8 3}{2 \cdot 3} : \frac{2 ( 3 - 2 3 )}{3}

The solutions to the quadratic equation are:

x = \frac{2 ( 3 + 2 3 )}{3}, x = \frac{2 ( 3 - 2 3 )}{3}

x^{2} - 6 = 138

s^{2} + 3.91 s + 14.846 = 0

2 (x - 3)^{2} + 10 = 24

2 x^{2} - 6 = x

(4 x + 3)^{2} = 0

What are the solutions to the equation 3x^2-12x-4=0 ?
The solutions to the equation 3x^2-12x-4=0 are x=(2(3+2sqrt(3)))/3 ,x=(2(3-2sqrt(3)))/3
Find the zeros of 3x^2-12x-4=0
The zeros of 3x^2-12x-4=0 are x=(2(3+2sqrt(3)))/3 ,x=(2(3-2sqrt(3)))/3