What are the solutions to the equation 3z^2-10z+2=2z^2 ?

The solutions to the equation 3z^2-10z+2=2z^2 are z=5+sqrt(23),z=5-sqrt(23)

Find the zeros of 3z^2-10z+2=2z^2

The zeros of 3z^2-10z+2=2z^2 are z=5+sqrt(23),z=5-sqrt(23)

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3 z^{2} - 10 z + 2 = 2 z^{2}

z = 5 + 23, z = 5 - 23

Decimal Notation

z = 9.79583 \dots, z = 0.20416 \dots

Solution steps

3 z^{2} - 10 z + 2 = 2 z^{2}

Move

2 z^{2}

to the left side

z^{2} - 10 z + 2 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 \cdot 1 \cdot 2}{2 \cdot 1}

(- 10)^{2} - 4 \cdot 1 \cdot 2 = 223

z_{1, 2} = \frac{- ( - 10 ) \pm 2 23}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 10 ) + 2 23}{2 \cdot 1}, z_{2} = \frac{- ( - 10 ) - 2 23}{2 \cdot 1}

z = \frac{- ( - 10 ) + 2 23}{2 \cdot 1} : 5 + 23

z = \frac{- ( - 10 ) - 2 23}{2 \cdot 1} : 5 - 23

The solutions to the quadratic equation are:

z = 5 + 23, z = 5 - 23

12 x^{2} - 96 x + 135 = 0

6 x - 9 - x^{2} = 0

16 x^{2} - 8 x + 145 = 0

- 4 x^{2} + 3 x = 0

x^{2} + (a + 3) x + a + 2 = 0

What are the solutions to the equation 3z^2-10z+2=2z^2 ?
The solutions to the equation 3z^2-10z+2=2z^2 are z=5+sqrt(23),z=5-sqrt(23)
Find the zeros of 3z^2-10z+2=2z^2
The zeros of 3z^2-10z+2=2z^2 are z=5+sqrt(23),z=5-sqrt(23)