What are the solutions to the equation 3z^2-8z+4=5z ?

The solutions to the equation 3z^2-8z+4=5z are z=4,z= 1/3

Find the zeros of 3z^2-8z+4=5z

The zeros of 3z^2-8z+4=5z are z=4,z= 1/3

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3 z^{2} - 8 z + 4 = 5 z

z = 4, z = \frac{1}{3}

Decimal Notation

z = 4, z = 0.33333 \dots

Solution steps

3 z^{2} - 8 z + 4 = 5 z

Move

5 z

to the left side

3 z^{2} - 13 z + 4 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 \cdot 3 \cdot 4}{2 \cdot 3}

(- 13)^{2} - 4 \cdot 3 \cdot 4 = 11

z_{1, 2} = \frac{- ( - 13 ) \pm 11}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- ( - 13 ) + 11}{2 \cdot 3}, z_{2} = \frac{- ( - 13 ) - 11}{2 \cdot 3}

z = \frac{- ( - 13 ) + 11}{2 \cdot 3} : 4

z = \frac{- ( - 13 ) - 11}{2 \cdot 3} : \frac{1}{3}

The solutions to the quadratic equation are:

z = 4, z = \frac{1}{3}

\frac{y ^{2}}{4} = \frac{3 y + 4}{4}

x^{2} + 8 x - 11 = 6 x - 8

y^{2} - 2 = - y

6 a^{2} + 8 a - 9 = 0

x^{2} + 5 x - 32 = 0

What are the solutions to the equation 3z^2-8z+4=5z ?
The solutions to the equation 3z^2-8z+4=5z are z=4,z= 1/3
Find the zeros of 3z^2-8z+4=5z
The zeros of 3z^2-8z+4=5z are z=4,z= 1/3