What are the solutions to the equation 3/2 z^2-4z-1=0 ?

The solutions to the equation 3/2 z^2-4z-1=0 are z=(4+sqrt(22))/3 ,z=(4-sqrt(22))/3

Find the zeros of 3/2 z^2-4z-1=0

The zeros of 3/2 z^2-4z-1=0 are z=(4+sqrt(22))/3 ,z=(4-sqrt(22))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{3}{2} z^{2} - 4 z - 1 = 0

z = \frac{4 + 22}{3}, z = \frac{4 - 22}{3}

Decimal Notation

z = 2.89680 \dots, z = - 0.23013 \dots

Solution steps

\frac{3}{2} z^{2} - 4 z - 1 = 0

Multiply both sides by

2

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

Solve with the quadratic formula

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

(- 8)^{2} - 4 \cdot 3 (- 2) = 222

z_{1, 2} = \frac{- ( - 8 ) \pm 2 22}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- ( - 8 ) + 2 22}{2 \cdot 3}, z_{2} = \frac{- ( - 8 ) - 2 22}{2 \cdot 3}

z = \frac{- ( - 8 ) + 2 22}{2 \cdot 3} : \frac{4 + 22}{3}

z = \frac{- ( - 8 ) - 2 22}{2 \cdot 3} : \frac{4 - 22}{3}

The solutions to the quadratic equation are:

z = \frac{4 + 22}{3}, z = \frac{4 - 22}{3}

1 2^{2} + 3 5^{2} = c^{2}

x^{2} - 18 x = 17

x^{2} + 72 = 0

x^{2} - 9 x - 70 = 0

x^{2} + 12 x - 12 = 0

What are the solutions to the equation 3/2 z^2-4z-1=0 ?
The solutions to the equation 3/2 z^2-4z-1=0 are z=(4+sqrt(22))/3 ,z=(4-sqrt(22))/3
Find the zeros of 3/2 z^2-4z-1=0
The zeros of 3/2 z^2-4z-1=0 are z=(4+sqrt(22))/3 ,z=(4-sqrt(22))/3