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

The solutions to the equation 3z^2-z-8=0 are z=(1+sqrt(97))/6 ,z=(1-sqrt(97))/6

Find the zeros of 3z^2-z-8=0

The zeros of 3z^2-z-8=0 are z=(1+sqrt(97))/6 ,z=(1-sqrt(97))/6

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3 z^{2} - z - 8 = 0

z = \frac{1 + 97}{6}, z = \frac{1 - 97}{6}

Decimal Notation

z = 1.80814 \dots, z = - 1.47480 \dots

Solution steps

3 z^{2} - z - 8 = 0

Solve with the quadratic formula

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

(- 1)^{2} - 4 \cdot 3 (- 8) = 97

z_{1, 2} = \frac{- ( - 1 ) \pm 97}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- ( - 1 ) + 97}{2 \cdot 3}, z_{2} = \frac{- ( - 1 ) - 97}{2 \cdot 3}

z = \frac{- ( - 1 ) + 97}{2 \cdot 3} : \frac{1 + 97}{6}

z = \frac{- ( - 1 ) - 97}{2 \cdot 3} : \frac{1 - 97}{6}

The solutions to the quadratic equation are:

z = \frac{1 + 97}{6}, z = \frac{1 - 97}{6}

2 (x^{2} + 7) = 30

- 6 x^{2} - 6 = - 7 x - 9

x^{2} - 10 x = 3

x^{2} - 10 x = 2

(x + 4) (x + 2) = 0

What are the solutions to the equation 3z^2-z-8=0 ?
The solutions to the equation 3z^2-z-8=0 are z=(1+sqrt(97))/6 ,z=(1-sqrt(97))/6
Find the zeros of 3z^2-z-8=0
The zeros of 3z^2-z-8=0 are z=(1+sqrt(97))/6 ,z=(1-sqrt(97))/6