What are the solutions to the equation -1/3 (4+z)z=-5/6 ?

The solutions to the equation -1/3 (4+z)z=-5/6 are z=-(4+sqrt(26))/2 ,z=(sqrt(26)-4)/2

Find the zeros of -1/3 (4+z)z=-5/6

The zeros of -1/3 (4+z)z=-5/6 are z=-(4+sqrt(26))/2 ,z=(sqrt(26)-4)/2

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- \frac{1}{3} (4 + z) z = - \frac{5}{6}

z = - \frac{4 + 26}{2}, z = \frac{26 - 4}{2}

Decimal Notation

z = - 4.54950 \dots, z = 0.54950 \dots

Solution steps

- \frac{1}{3} (4 + z) z = - \frac{5}{6}

Find Least Common Multiplier of

3, 6 : 6

Multiply by LCM=

6

- \frac{1}{3} (4 + z) z \cdot 6 = - \frac{5}{6} \cdot 6

Simplify

- 2 z (4 + z) = - 5

Expand

- 2 z (4 + z) : - 8 z - 2 z^{2}

- 8 z - 2 z^{2} = - 5

Move

5

to the left side

- 8 z - 2 z^{2} + 5 = 0

Write in the standard form

a x^{2} + b x + c = 0

- 2 z^{2} - 8 z + 5 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 ( - 2 ) \cdot 5}{2 ( - 2 )}

(- 8)^{2} - 4 (- 2) \cdot 5 = 226

z_{1, 2} = \frac{- ( - 8 ) \pm 2 26}{2 ( - 2 )}

Separate the solutions

z_{1} = \frac{- ( - 8 ) + 2 26}{2 ( - 2 )}, z_{2} = \frac{- ( - 8 ) - 2 26}{2 ( - 2 )}

z = \frac{- ( - 8 ) + 2 26}{2 ( - 2 )} : - \frac{4 + 26}{2}

z = \frac{- ( - 8 ) - 2 26}{2 ( - 2 )} : \frac{26 - 4}{2}

The solutions to the quadratic equation are:

z = - \frac{4 + 26}{2}, z = \frac{26 - 4}{2}

(6 - 5 i) (4 - 3 i)

\frac{16}{3} - 5

- x^{2} - x + 1 = 0

x - 2 = 2

- \frac{60}{2}

What are the solutions to the equation -1/3 (4+z)z=-5/6 ?
The solutions to the equation -1/3 (4+z)z=-5/6 are z=-(4+sqrt(26))/2 ,z=(sqrt(26)-4)/2
Find the zeros of -1/3 (4+z)z=-5/6
The zeros of -1/3 (4+z)z=-5/6 are z=-(4+sqrt(26))/2 ,z=(sqrt(26)-4)/2