What are the solutions to the equation 1/2 z^2+5/6 z=0 ?

The solutions to the equation 1/2 z^2+5/6 z=0 are z=0,z=-5/3

Find the zeros of 1/2 z^2+5/6 z=0

The zeros of 1/2 z^2+5/6 z=0 are z=0,z=-5/3

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\frac{1}{2} z^{2} + \frac{5}{6} z = 0

z = 0, z = - \frac{5}{3}

Decimal Notation

z = 0, z = - 1.66666 \dots

Solution steps

\frac{1}{2} z^{2} + \frac{5}{6} z = 0

Find Least Common Multiplier of

2, 6 : 6

Multiply by LCM=

6

\frac{1}{2} z^{2} \cdot 6 + \frac{5}{6} z \cdot 6 = 0 \cdot 6

Simplify

3 z^{2} + 5 z = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

5^{2} - 4 \cdot 3 \cdot 0 = 5

z_{1, 2} = \frac{- 5 \pm 5}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- 5 + 5}{2 \cdot 3}, z_{2} = \frac{- 5 - 5}{2 \cdot 3}

z = \frac{- 5 + 5}{2 \cdot 3} : 0

z = \frac{- 5 - 5}{2 \cdot 3} : - \frac{5}{3}

The solutions to the quadratic equation are:

z = 0, z = - \frac{5}{3}

2 y^{2} - 8 y - 10 = 0

183000 x^{2} - 1400000 x - 22912000 = 0

24 x^{2} - 3 x - 11 = 0

12 x^{2} - 168 x + 432 = 0

x, z = y x^{2} z^{2} - x y^{4} + x y

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