What are the solutions to the equation 3x^2-8x-12=0 ?

The solutions to the equation 3x^2-8x-12=0 are x=(2(2+sqrt(13)))/3 ,x=(2(2-sqrt(13)))/3

Find the zeros of 3x^2-8x-12=0

The zeros of 3x^2-8x-12=0 are x=(2(2+sqrt(13)))/3 ,x=(2(2-sqrt(13)))/3

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3 x^{2} - 8 x - 12 = 0

x = \frac{2 ( 2 + 13 )}{3}, x = \frac{2 ( 2 - 13 )}{3}

Decimal Notation

x = 3.73703 \dots, x = - 1.07036 \dots

Solution steps

3 x^{2} - 8 x - 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 3 ( - 12 )}{2 \cdot 3}

(- 8)^{2} - 4 \cdot 3 (- 12) = 413

x_{1, 2} = \frac{- ( - 8 ) \pm 4 13}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 13}{2 \cdot 3}, x_{2} = \frac{- ( - 8 ) - 4 13}{2 \cdot 3}

x = \frac{- ( - 8 ) + 4 13}{2 \cdot 3} : \frac{2 ( 2 + 13 )}{3}

x = \frac{- ( - 8 ) - 4 13}{2 \cdot 3} : \frac{2 ( 2 - 13 )}{3}

The solutions to the quadratic equation are:

x = \frac{2 ( 2 + 13 )}{3}, x = \frac{2 ( 2 - 13 )}{3}

x^{2} + 30 = 24 x - 114

0 = - 407 x^{2} + 220275 x - 19824750

4 x^{2} + 28 x = 72

x^{2} = 5 (x - 1.2)

z^{2} + 2 + 1 = 0

What are the solutions to the equation 3x^2-8x-12=0 ?
The solutions to the equation 3x^2-8x-12=0 are x=(2(2+sqrt(13)))/3 ,x=(2(2-sqrt(13)))/3
Find the zeros of 3x^2-8x-12=0
The zeros of 3x^2-8x-12=0 are x=(2(2+sqrt(13)))/3 ,x=(2(2-sqrt(13)))/3