What are the solutions to the equation 5/3 z^2-4z-1=0 ?

The solutions to the equation 5/3 z^2-4z-1=0 are z=(6+sqrt(51))/5 ,z=(6-sqrt(51))/5

Find the zeros of 5/3 z^2-4z-1=0

The zeros of 5/3 z^2-4z-1=0 are z=(6+sqrt(51))/5 ,z=(6-sqrt(51))/5

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\frac{5}{3} z^{2} - 4 z - 1 = 0

z = \frac{6 + 51}{5}, z = \frac{6 - 51}{5}

Decimal Notation

z = 2.62828 \dots, z = - 0.22828 \dots

Solution steps

\frac{5}{3} z^{2} - 4 z - 1 = 0

Multiply both sides by

3

5 z^{2} - 12 z - 3 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 5 ( - 3 )}{2 \cdot 5}

(- 12)^{2} - 4 \cdot 5 (- 3) = 251

z_{1, 2} = \frac{- ( - 12 ) \pm 2 51}{2 \cdot 5}

Separate the solutions

z_{1} = \frac{- ( - 12 ) + 2 51}{2 \cdot 5}, z_{2} = \frac{- ( - 12 ) - 2 51}{2 \cdot 5}

z = \frac{- ( - 12 ) + 2 51}{2 \cdot 5} : \frac{6 + 51}{5}

z = \frac{- ( - 12 ) - 2 51}{2 \cdot 5} : \frac{6 - 51}{5}

The solutions to the quadratic equation are:

z = \frac{6 + 51}{5}, z = \frac{6 - 51}{5}

8 x^{2} - 5 = 11

z^{2} = 3

x^{2} = \frac{x ^{2}}{2} + 2

x = x^{2} - 12 x + 36

x^{2} - 10 x + 15 = - 7

What are the solutions to the equation 5/3 z^2-4z-1=0 ?
The solutions to the equation 5/3 z^2-4z-1=0 are z=(6+sqrt(51))/5 ,z=(6-sqrt(51))/5
Find the zeros of 5/3 z^2-4z-1=0
The zeros of 5/3 z^2-4z-1=0 are z=(6+sqrt(51))/5 ,z=(6-sqrt(51))/5