What are the solutions to the equation 3*z^2+20*z-11=0 ?

The solutions to the equation 3*z^2+20*z-11=0 are z=(-10+sqrt(133))/3 ,z=-(10+sqrt(133))/3

Find the zeros of 3*z^2+20*z-11=0

The zeros of 3*z^2+20*z-11=0 are z=(-10+sqrt(133))/3 ,z=-(10+sqrt(133))/3

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3 \cdot z^{2} + 20 \cdot z - 11 = 0

z = \frac{- 10 + 133}{3}, z = - \frac{10 + 133}{3}

Decimal Notation

z = 0.51085 \dots, z = - 7.17752 \dots

Solution steps

3 z^{2} + 20 z - 11 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- 20 \pm 2 0 ^{2} - 4 \cdot 3 ( - 11 )}{2 \cdot 3}

2 0^{2} - 4 \cdot 3 (- 11) = 2133

z_{1, 2} = \frac{- 20 \pm 2 133}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- 20 + 2 133}{2 \cdot 3}, z_{2} = \frac{- 20 - 2 133}{2 \cdot 3}

z = \frac{- 20 + 2 133}{2 \cdot 3} : \frac{- 10 + 133}{3}

z = \frac{- 20 - 2 133}{2 \cdot 3} : - \frac{10 + 133}{3}

The solutions to the quadratic equation are:

z = \frac{- 10 + 133}{3}, z = - \frac{10 + 133}{3}

2 x^{2} + 36 = 0

\frac{i}{i}

2 (1.5 x - 2.1) + 1.7 \geq 2 (2.4 x - 3.5)

3 x^{2} - 4 x + 6 = 2

- \frac{2}{3} (0) - 1

What are the solutions to the equation 3*z^2+20*z-11=0 ?
The solutions to the equation 3*z^2+20*z-11=0 are z=(-10+sqrt(133))/3 ,z=-(10+sqrt(133))/3
Find the zeros of 3*z^2+20*z-11=0
The zeros of 3*z^2+20*z-11=0 are z=(-10+sqrt(133))/3 ,z=-(10+sqrt(133))/3