What are the solutions to the equation 3z^2-3z=-5 ?

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

Find the zeros of 3z^2-3z=-5

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

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

z = \frac{1}{2} + i \frac{51}{6}, z = \frac{1}{2} - i \frac{51}{6}

Solution steps

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

Move

5

to the left side

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

Solve with the quadratic formula

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

Simplify

(- 3)^{2} - 4 \cdot 3 \cdot 5 : 51 i

z_{1, 2} = \frac{- ( - 3 ) \pm 51 i}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- ( - 3 ) + 51 i}{2 \cdot 3}, z_{2} = \frac{- ( - 3 ) - 51 i}{2 \cdot 3}

z = \frac{- ( - 3 ) + 51 i}{2 \cdot 3} : \frac{1}{2} + i \frac{51}{6}

z = \frac{- ( - 3 ) - 51 i}{2 \cdot 3} : \frac{1}{2} - i \frac{51}{6}

The solutions to the quadratic equation are:

z = \frac{1}{2} + i \frac{51}{6}, z = \frac{1}{2} - i \frac{51}{6}

\frac{100}{49}

x^{2} + 14 x + 8 = 0

x^{2} - 4 x = 77

\frac{1}{3}

42 x^{2} - 69 x + 20 = 7 x^{2} - 8

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